Football's world governing body FIFA has agreed to allow the introduction of goal-line technology after it was approved by the International FA Board.
Two systems, Hawk-Eye and GoalRef, have been approved by the IFAB after passing a series of scientific tests set by FIFA.
Technology could be introduced into the Premier League as soon as the new year following the decision at a meeting in Zurich.
FIFA general secretary Jerome Valcke said they intended to bring goal-line technology in for the Club World Cup in Japan in December, next year's Confederations Cup and the 2014 World Cup in Brazil.
Valcke said FIFA would pay for the systems - around $250,000 US per stadium - and leave them in place in the stadiums.
"We want to make sure that the systems at the World Cup work at 150 percent, not 90 percent," Valcke said.
FA general secretary Alex Horne told a news conference in Zurich it was "a hugely important day" for football.
He said: "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 - the scoring of a goal."
Scottish FA chief executive Stewart Regan hailed the decision, saying: "Over the past few years there have been a number of occasions where mistakes have been made in football.
"The referee will still make the final decision but the view of the board is that anything that can help the referee has to be good.
"I think this is an historic day for football and I'm delighted to be part of that decision made today."
Patrick Nelson, chief executive of the Irish FA, added: "The three decisions made today will be long-lasting and will resonate throughout the world.
"The IFAB has been around since 1886 and has been the guardians of the laws of the game for all that time, and has developed the game slowly and carefully and conservatively.
"But this is a momentous day, the beginning of something new in football."
Jonathan Ford, chief executive of the Football Association of Wales, also backed the decision, which was made unanimously.
Ford said: "The Football Association of Wales is extremely proud to be a member of this board and has devoted a great deal of time and deliberation and effort to this.
"Fundamental and momentous decisions were made here today and we are very proud to be involved with that."
The IFAB - made up of FIFA and the four home nations - ruled out any video replays of goal-line decisions being shown on TV or on big screens to the crowd at stadiums, as happens with the Hawk-Eye system in tennis.
Ford stressed the referee had the final say on whether to award a goal and pointed out he may decide to rule it out for other reasons even if the technology shows the ball has crossed the line.
"If a giant screen comes up 'goal' but it is offside then could have a major issue with crowd management," said Ford.
Regan added: "This is not designed to be put on giant screens, this is about technology designed to help the referee."
And the Premier League wasted no time in hailing the decision, releasing a statement straight after the announcement saying that the technology will be introduced in to England's top division as quickly as possible.
"The Premier League has been a long term advocate of goal-line technology," the statement read.
"We welcome today's decision by IFAB and will engage in discussions with both Hawkeye and GoalRef in the near future with a view to introducing goal-line technology as soon as is practically possible."
Approval was also given on the five officials method of refereeing matches.
The referee and two linesmen will be aided by two further officials posted behind each team's goal-line to keep an eye on action in and around the critical penalty box area should tournament organisers want it.
FIFA has been trialling the 'Additional Assitant Referee' system since 2008 and it was in use during the recently-finished Euro 2012 as well as the UEFA Champions League.