VAR has been trialled in some domestic English cup games this season, and has been used in Germany and Italy.
The International Football Association Board (Ifab) "unanimously approved" its introduction on a permanent basis after a meeting in Zurich on Saturday.
Leagues and competitions must now apply to Ifab to implement the system.
Fifa president Gianni Infantino said a decision on whether VAR would be used at the World Cup will be taken at a meeting on 16 March.
"As of today, video assistant refereeing is part of football," he said.
"We hope and encourage a favourable decision in this respect because we are very positive about VAR."
One of the concerns over VAR is that those watching are uncertain about what is going on, but Fifa says it is working on a system that will provide information to the "giant screen operators as well as broadcasters and commentators" about the reason and outcome of a review.
"What is our idea (for the World Cup) is that after the final decision is taken by the referee on the pitch we would like to show in the stadium the selected replay that was used by the referee and VAR," said Johannes Holzmuller, head of Fifa football technology innovation.