David Goodwillie has completed his transfer to Blackburn Rovers after signing a four-year deal.
The 22-year-old striker moves from Dundee United for an undisclosed fee, thought to be £2m plus £800,000 in potential add-ons.
Rovers said they had beaten "fierce competition from a host of clubs" for the Scotland international.
Rangers had made several last-ditch bids for the striker which were rejected by Dundee United.
"I think it's a massive stage to further my career and there's no better place to play than the Premiership," Goodwillie said.
"Growing up you want to play in the Premiership and I'm really grateful to have that opportunity.
"I think it's every young boy's dream to play in England at some point in their career.
"I feel ready, and it's up to the manager and we'll see what happens."
On Tuesday, Rangers manager Ally McCoist claimed the Scottish champions had matched Blackburn's offer.
But United insisted that, although closer to Rovers' figure, it had still fallen short of their demands.
Tannadice chairman Stephen Thompson told BBC Scotland: "Rangers' bid was not acceptable and the overall deal was not as much as was on offer from Blackburn."
Blackburn were given permission to talk to Goodwillie at the weekend after having their bid accepted by Thompson.
However, the player's planned medical was postponed on Monday and Rangers increased their offer having had a fourth bid rejected 24 hours earlier.
Asked if it matched Blackburn's bid for the Scotland international, McCoist said: "As far as I'm aware, yes.
"We believe that we have put a bid in that's more than acceptable.
"We've all made no secret of the fact that David is a player we would love to see at Rangers."
Goodwillie, who was named on Tuesday in Craig Levein's Scotland squad to face Denmark next week, was omitted from United's squad to face Hearts on Sunday as he and his agent talked to Rovers.