The use of the technology, which helps match officials determine whether the ball has entered the goal in cases where it cannot easily be seen by the naked eye, was approved at an executive committee meeting, UEFA said in a statement.
UEFA said it would continue to employ additional assistant referees, one on each goal-line, to monitor all activity in and around the penalty area, a system pioneered by European football's governing body.
Goal-line technology would be used in the Champions League from the final qualifying round but not in the first three preliminary rounds. It could also be introduced in the Europa League from 2017-18.
Football's rule-makers, the International Football Association Board (IFAB), first approved the use of goal-line technology in 2012.
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It was introduced in the English Premier League in the 2013-14 season and was used at the World Cup for the first time in 2014. It has also been adopted by the Bundesliga in Germany and Serie A in Italy.
UEFA president Michel Platini, a former France captain who describes himself as an old romantic, had opposed the use of goal-line technology, saying it would strip the sport of its human element and open a "Pandora's box" of other technology.
However, Platini was banned for eight years by the ethics committee of football's world governing body in December over a 2 million Swiss francs (£1.38 million) payment he received from FIFA in 2011.
"This will dispel any doubts about whether a goal has been scored," UEFA general secretary Gianni Infantino told reporters. "We looked at it seriously and finally we decided to start with the Euro and then move on to the Champions League."
There have been a growing number of calls from players and managers to use video technology in other aspects of the game.
Earlier this month the IFAB decided to recommend trialling video replays next season to help referees with questionable goals, penalties, red cards and cases of mistaken identity.
The IFAB will recommend to its AGM in March that trials get underway with a view to the system becoming law in two to three years.
(Reporting by Ed Osmond and Brian Homewood; editing by John Stonestreet and Ken Ferris)
