After months of testing, the International FA Board (IFAB) approved by a unanimous vote both the Hawk-Eye and the GoalRef systems at a meeting in Zurich.
FIFA general secretary Jerome Valcke announced that both systems will be tested extensively at the FIFA Club World Cup in Japan this December.
The vote means that the Premier League and Football Association are a step closer to getting the green light to introducing the technology into their competitions.
Chelsea manager Roberto Di Matteo said a system was needed as soon as possible.
"We see every season, every big tournament, we need it because there are some crucial moments within those games where with a bit of technology you could find the right solution," he said.
There will still be a delay before either system can be used in competitive football however - each will need to be licensed, installed and then tested in every venue to make sure it is working properly.
The IFAB also insists that the technology is used only as an aid to referees to make a decision, rather than being the deciding factor in whether the ball has crossed the line. It means referees can still decide not to award a goal based on what they see even if the systems are indicating the ball has crossed the line.
FIFA's president Sepp Blatter is now a firm supporter of goal-line technology, having changed his mind after Frank Lampard's disallowed goal for England against Germany in the 2010 World Cup (pictured).
The clamour increased last month after Ukraine's disallowed goal against England and has also served to sweep aside any lingering doubts over the systems' margins of error.
The body also voted that the UEFA experiment with extra officials can be continued by organisers who wished to do so, and the wearing of Islamic headscarves for female footballers.
"Safety and medical issues have been removed for the use of the headscarf and it is approved that players can have the headscarf," Valcke said.