There are a few hurdles still to negotiate, but it could be introduced into the English Premier League midway through the 2012-13 season.
Here, BBC Sport asks - and answers - the big questions.
So, after years of debate, is goal-line technology going to be introduced at all matches?
The International Football Association Board voted unanimously in favour of introducing the technology, leaving it up to individual associations to decide whether to implement it into their respective competitions.
Speaking to BBC Sport this week,
Blatter said: "That was the moment for me to say: 'You can't afford for something similar to happen in the next World Cup.' We could say it is a historic day for international football."
So once Fifa changed its stance, how did it go about finding a suitable system?
Eight systems were initially tested by an independent body. Each company had to demonstrate their technology adhered to Fifa benchmarks. These included notification of a goal being sent to the referee's watch within one second of the ball crossing the line and strict standards on accuracy. Two companies proceeded to the second phase of testing.
GoalRef and British-based Hawk-Eye were tested again to check their accuracy in "real-world" scenarios - including in poor weather conditions, while floodlights are being used and when players are moving or standing close to the goal posts. They were both successful.
Tell me more about the two systems that have been approved.
Hawk-Eye's system uses six cameras, focusing on each goal, to track the ball on the pitch. The system's software 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. The whole process takes less than a second to complete.
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.
So two companies have been approved - what happens now?
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 wants to use it "as soon as practically possible". It will decide, through consultation with member clubs, its preferred system and then make a decision about cost and when to implement it. The Football League will also discuss the matter with its 72 clubs.
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There are big questions for the FA, including whether the systems would be allowed in the FA Cup. Top-flight clubs could, for example, use goal-line technology for home ties, but it might not be available to teams from lower divisions.
And what about the Champions League? Isn't Uefa against it?
Uefa president Michel Platini believes it is wrong to implement goal-line technology due to the infrequency of goal-line incidents within games. It means there could be a situation where technology is used in Premier League and World Cup games but not the Champions League and Europa League. However, Blatter is confident Platini, who is in favour of using more assistant referees instead, will change his mind.
"He is more afraid that once technology comes in, it will go from the goal-line towards the penalty box or whatever," said Blatter. "But I am sure with this unanimous decision of the international board that he will follow. He cannot go against history and this is new history."
Who is paying for it?
That is another unanswered question. The Premier League is likely to centrally fund it for its member clubs, but what about everybody else? Commercial sponsorship is another possibility and it is believed the Football League could look at that option.
Then there is international competition. England would happily pay for goal-line technology, but a smaller nation may not have the funds or not want it. That is when the issue might become complicated. So England could have it and others would not.
And how much will it cost?
Fifa general secretary Jerome Valcke has estimated the cost to be between £120,000 and £160,000 for each system. However, he said he expects that figure to fall over time.
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