The officials famously missed this 'goal' at Old Trafford by Pedro Mendes in 2005.
HumanIPO reported earlier this week clubs were set to vote on whether to adopt the system at a meeting of the 20 Premier League chairmen yesterday.
The Football Association (FA) will now install the Hawk-Eye system, which claims to be “millimetre accurate, ensuring no broadcast replays could disprove the decision”, at Wembley in time for the Community Shield in August.
World football governing body FIFA announced in February it would implement goal-line technology during the 2014 World Cup in Brazil.
England manager Roy Hodgson welcome the decision, telling the BBC it would put an end to “gross injustices” in the English game.
“It is something that people in football have wanted for a long time. There's been a big debate, and for a while it was pushed back but now everyone's on the same page and we've introduced it,” he said.
“At least it will stop some of those gross injustices that we have seen in recent years where goals have obviously been scored and not allowed.”
Hawk-Eye inventor Paul Hawkins told the BBC there was no chance the new technology would slow down matches, with the system notifying the referee with a vibration and an optical signal within one second of a ball crossing the line.
“It will not slow the game down - it is not going to become like rugby,” he said. “In under a second we will provide the information to the watch, then afterwards we will show a TV replay that will definitively prove what we showed the referee was correct.
“Football's a great game. It does not need enhancements to add to the drama. Our technology is there to ensure decisions are correct.”
BBC Sport’s Richard Conway said some involved in football hope this decision will herald a technological revolution in the sport.
“Off-side decisions and contentious fouls could also benefit from video analysis, something that Fifa insist will not happen,” he wrote. “But many believe that the game has opened Pandora's box by approving systems for goal-line decisions.”
