All third-round matches last weekend were delayed by one minute to publicise the FA's "Heads Up" mental health campaign, backed by FA president Prince William.
That jarred with the streaming agreement given the link between gambling addiction and mental health issues.
The government on Wednesday urged the FA to reconsider the agreement and the decision to allow the matches to be streamed free elsewhere removes the need to hold an active gambling account to watch the games.
Sports minister Nigel Adams welcomed the move and said it was up to the FA and IMG to ensure fans could see the games without needing to register or to place a bet.
"Our members did not seek exclusivity for the rights to screen FA Cup games," said a statement from Brigid Simmonds, who chairs Betting and Gaming Council (BGC).
"They are therefore happy for IMG to offer the rights to screen these games to the Football Association or another appropriate body so that the games can be viewed for free by the public with immediate effect."
The statement from the BGC was supported by bet365, GVC, Flutter, William Hill and Kindred, who held the streaming rights.