Goal-line technology could be introduced in the Premier League midway through the 2012-13 season after it was approved by the International Football Association Board (IFAB) in Zurich.
Two systems - Hawk-Eye and GoalRef - have passed Fifa's criteria for use.
The technology will first be used at December's Fifa Club World Cup and, if successful, at the 2013 Confederations Cup and 2014 World Cup.
The Premier League said it wanted it "as soon as practically possible".
A statement following IFAB's announcement added: "The Premier League has been a long-term advocate of goal-line technology.
How does Hawk-Eye work?
Hawk-Eye's system works by using six cameras, focusing on each goal, to track the ball on the pitch.
The system's software then uses "triangulation" to pinpoint the exact location of the ball.
If it crosses the goal-line an encrypted radio signal is sent to the referee's wristwatch to indicate a goal has been scored.
In line with Fifa's requirements, the whole process takes less than a second to complete.
"We welcome today's decision by IFAB and will engage in discussions with both Hawk-Eye and GoalRef in the near future with a view to introducing goal-line technology as soon as is practically possible."
FA general secretary Alex Horne said it was up to the Premier League, which is likely to centrally fund the technology for its member clubs, to decide on a timescale for implementation.
"It may be December until the technology is absolutely finally approved and installed in stadia," he said at a press conference in Zurich. "Priority is given to the Fifa Club World Cup in Japan.
"The Premier League need to talk to the two [technology providers] and the clubs. My understanding is that clubs are supportive and, in principle, as long as all clubs agree it could be introduced part-way through the season - it could be before the start of 2013-14 season, it could be part-way through.
"We have already got Hawk-Eye at Wembley. It needs to be calibrated and make sure it's working properly and licensed so we are nearly there and we could turn it on on quite quickly.
"The FA Cup would be our decision and we could say for the semi-finals and finals of the FA Cup we could turn it on. I don't think that is a very controversial decision."
Horne added that he felt it was "a hugely important day" for football.
"We believe that it is a great day for football. From an English perspective, today is a hugely important day. It is a cause we have had on our agenda for a number of years.
"This is about having the right technology helping the referee in a relatively rare occurrence."
How does GoalRef work?
GoalRef uses a microchip implanted in the ball and the use of low magnetic waves around the goal.
The system then detects any change in the magnetic field on or behind the goal-line to determine if a goal has been scored.
The process takes less than one second, with the result electronically relayed to the referee.
The systems will require testing after they are installed in each stadium to ensure they are working properly before they can be used, with licenses lasting for 12 months.
Premier League director of communications Dan Johnson said there were several factors to consider before the system is implemented.
"We have to look at the technologies ourselves and decide which is the most appropriate," he said.
"There is the cost factor too - which is why we are particularly pleased that two companies have come through because it provides some competitive tension.
"We haven't ruled out introducing it midway through the season, but it is dependent on what type of progress we make with the two companies, what we think of the technology and how our clubs react.
"One thing which wasn't clear [in the Zurich meeting] was a graphical representation of the technology working because I think it is important fans and television viewers can see it working. It is important for the trust in the technology."
The Football League said it "welcomed the decision" and will now consider the future use of technology in its competitions.
It is believed it could look to fund it through commercial sponsorship.
The IFAB was keen to stress that technology will not be used to help referees make any other decisions.
The momentum for the introduction of goal-line technology increased after Ukraine were denied an equaliser after
the ball appeared to cross the line
1-0 defeat by England
at Euro 2012.
Goal-line technology gets the go-ahead
Chelsea manager Roberto Di Matteo said: "We see every season, every big tournament, we need it because there are some crucial moments within those games where you could find the right solution with a bit of technology."
Uefa president Michel Platini is believed to prefer the use of five match officials, something which was also approved by Fifa on Thursday.
The system, which sees an extra official posted behind each goal-line to monitor action in and around the penalty box, has been on trial since 2008 and was in use during Euro 2012 as well as last season's Champions League.
Football's governing body also lifted a ban on women wearing headscarves during games, clearing the way for the participation of many Islamic nations in top-flight competition.