James Collins' first-half header proved enough to earn Shrewsbury Town promotion to League One.
Graham Turner's men were deserved victors as they restored Town to the third tier of English football for the first time in 15 years.
But Swindon's home win over Port Vale ended any slim hopes of the League Two title for Town, who will now go up in second place.
Collins struck the only goal on 38 minutes, nodding in Nicky Wroe's cross.
In Turner's second season of his second spell as Shrewsbury boss, the former Aston Villa, Wolves and Hereford manager's triumph comes 33 years after his first promotion with the Shropshire club, who he led up to the old Division Two in 1979.
Salop on the up again?
Promoted to Division Three - under Arthur Rowley, 1959
Promoted to Division Three - under Alan Durban, 1975
Promoted to Division Two - under Graham Turner, 1979
Promoted to Division Two - under Fred Davies, 1994
Promoted back to Football League - under Jimmy Quinn, 2004
Promoted to League One - under Graham Turner, 2012
It was also the 64-year-old's sixth successful promotion campaign, having also twice taken sides up with Wolves and Hereford United.
In front of a sell-out crowd, Shrewsbury's victory also ensured that they have gone unbeaten all season at the Greenhous Meadow, where they have not lost now since 1 March 2011.
Shrewsbury made much of the running from the first whistle, skipper Ian Sharps curling an early shot just wide from the edge of the box before Jermaine Grandison's header from a Matt Richards corner was cleared off the line by Brian Woodall.
Dagenham's only first-half chance came when Medi Elito's 20-yard drive drifted narrowly wide.
But the breakthrough Shrewsbury craved eventually came when Wroe's angled cross was headed home by top scorer Collins for his 16th goal of the season.
Home winger Mark Wright bent a shot just wide in the closing stages as Shrewsbury stretched their timely unbeaten late season run to nine matches.
At the other end, Shrewsbury registered their 19th clean sheet of the campaign, with keeper Chris Neal never seriously tested before the champagne corks were allowed to pop.
FROM THE DRESSING ROOM
Shrewsbury Town boss Graham Turner told BBC Radio Shropshire:
"It was a surprise when we went up in 1979. And the expectations were greater this season, but we've got there in the end.
"I don't know if the game lived up to expectations. I know one or two more goals going in would have helped us breathe a little easier, but results went our way elsewhere.
"We were sound and solid defensively, but the occasion and the result were more important.
"And I've got to pay tribute to the players. They've been fantastic all season. For all the hard work they've put in, they deserve everything they've got."
Full Time The game is over, as the referee blows his whistle.
The ball is sent over by Nicky Wroe, save by Chris Lewington.
The ball is delivered by Scott Doe, Nicky Wroe manages to make a clearance.
Scott Doe sends in a cross, clearance by Shane Cansdell-Sherriff.
The ball is crossed by Peter Gain.
Foul by Marvin Morgan on Michael Spillane, free kick awarded. Chris Lewington takes the direct free kick.
Unfair challenge on Joe Jacobson by Josh Scott results in a free kick. Direct free kick taken by Mark Wright.
Substitution Jon Taylor on for Aaron Wildig.
Mark Wright takes a shot. Blocked by Michael Spillane.
Dominic Green produces a cross, Headed effort from deep inside the penalty area by Josh Scott misses to the left of the goal.
Peter Gain produces a cross.
Substitution Ahmed Abdulla joins the action as a substitute, replacing Brian Woodall.
Mark Wright has an effort at goal from outside the box which goes wide right of the target.
Inswinging corner taken right-footed by Mark Wright from the left by-line, save by Chris Lewington.
Substitution Dominic Green on for Billy Bingham.
Substitution Medy Elito goes off and Peter Gain comes on.
Marvin Morgan delivers the ball, Abu Ogogo manages to make a clearance. Inswinging corner taken by Matthew Richards.
Substitution Marvin Morgan on for Terry Gornell.
Inswinging corner taken by Mark Wright from the left by-line.
Unfair challenge on Mathieu Baudry by James Collins results in a free kick. Free kick taken by Chris Lewington.
Brian Woodall is caught offside. Chris Neal takes the indirect free kick.
Jermaine Grandison crosses the ball, Scott Doe makes a clearance.
Centre by Medy Elito, Jermaine Grandison makes a clearance.
Centre by Abu Ogogo, clearance made by Joe Jacobson.
Corner taken left-footed by Damien McCrory from the right by-line to the near post, Mark Wright makes a clearance.
Luke Howell takes a shot. Inswinging corner taken left-footed by Damien McCrory played to the near post, clearance made by Joe Jacobson.
The ball is crossed by Scott Doe, save made by Chris Neal.
Medy Elito takes a shot. Joe Jacobson gets a block in. Corner taken by Damien McCrory from the right by-line played to the near post.
Free kick awarded for an unfair challenge on Mathieu Baudry by Terry Gornell. Direct free kick taken by Mathieu Baudry.
Luke Howell concedes a free kick for a foul on Ian Sharps. Direct free kick taken by Chris Neal.
Terry Gornell takes a shot. Save by Chris Lewington.
The ball is swung over by James Collins.
The ball is delivered by Jermaine Grandison, Terry Gornell has an effort at goal from close in which goes wide right of the target.
Unfair challenge on Nicky Wroe by Abu Ogogo results in a free kick. Direct free kick taken by Joe Jacobson.
Damien McCrory takes a inswinging corner to the near post, Terry Gornell manages to make a clearance.
Ian Sharps gives away a free kick for an unfair challenge on Josh Scott. Damien McCrory takes the free kick.
Centre by Mark Wright.
Abu Ogogo takes a shot. Save made by Chris Neal.
The referee blows his whistle to start the second half.
45:00 +1:06 Half time
Half Time The ref blows to end the first period.
Mathieu Baudry fouled by Terry Gornell, the ref awards a free kick. Mathieu Baudry takes the free kick.
The ball is delivered by Mark Wright.
The assist for the goal came from Nicky Wroe.
37:11 Goal scored
Goal! - James Collins - Shrewsbury 1 - 0 Dag & Red James Collins scores a headed goal from inside the box. Shrewsbury 1-0 Dag & Red.
The ball is crossed by Nicky Wroe,
Mark Wright takes a inswinging corner from the left by-line to the near post, Billy Bingham manages to make a clearance.
The ball is crossed by Ian Sharps, Scott Doe manages to make a clearance.
Shot by Luke Howell from outside the area goes high over the crossbar.
Matthew Richards crosses the ball, Damien McCrory makes a clearance.
The ball is swung over by Billy Bingham, clearance by Ian Sharps.
The ball is sent over by Joe Jacobson, Mathieu Baudry manages to make a clearance.
Luke Howell is penalised for a handball. Direct free kick taken by Chris Neal.
James Collins is ruled offside. Chris Lewington takes the indirect free kick.
Medy Elito produces a left-footed shot from just outside the box that misses to the right of the target.
James Collins crosses the ball, Michael Spillane gets a block in.
Shot by Nicky Wroe from outside the box goes high over the target.
Corner taken by Matthew Richards from the right by-line, Jermaine Grandison takes a shot. Mathieu Baudry manages to make a clearance.
A cross is delivered by Mark Wright, Damien McCrory manages to make a clearance.
Handball decision goes against Luke Howell. Mark Wright takes the direct free kick.
Joe Jacobson sends in a cross.
Free kick awarded for a foul by Michael Spillane on Terry Gornell. Joe Jacobson restarts play with the free kick.
The ball is swung over by Mark Wright, clearance made by Scott Doe. Inswinging corner taken from the left by-line by Mark Wright, Terry Gornell gives away a free kick for an unfair challenge on Michael Spillane. Chris Lewington restarts play with the free kick.
The ball is sent over by Scott Doe, clearance made by Jermaine Grandison.
The ball is crossed by Brian Woodall, Ian Sharps manages to make a clearance.
Jermaine Grandison fouled by Josh Scott, the ref awards a free kick. Free kick taken by Matthew Richards.
Centre by Scott Doe.
Free kick awarded for an unfair challenge on Billy Bingham by Terry Gornell. Mathieu Baudry restarts play with the free kick.
Centre by Nicky Wroe, Shot from just outside the box by Mark Wright misses to the left of the goal.
Joe Jacobson delivers the ball, Josh Scott manages to make a clearance.
The ball is swung over by Mark Wright, clearance made by Damien McCrory.
Ian Sharps produces a right-footed shot from just outside the box that goes wide right of the goal.
Corner taken by Matthew Richards, clearance made by Mathieu Baudry.
The ball is crossed by Mark Wright, Damien McCrory makes a clearance.
The ball is delivered by Mark Wright.
The ball is delivered by Scott Doe, clearance made by Shane Cansdell-Sherriff. Effort from outside the penalty area by Damien McCrory goes wide left of the goal.
Josh Scott sends in a cross, Shane Cansdell-Sherriff manages to make a clearance.
Terry Gornell is flagged offside by the assistant referee. Indirect free kick taken by Chris Lewington.
The ball is crossed by Medy Elito, Chris Neal makes a save.
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