The Spanish side made the offer last week and the Blues agreed on the deal after Gallagher made it clear that the move would be right for him.
The 24-year-old is expected to fly out to Madrid to complete his medical and sign the contract that would end his 18-year history at the club after he signed for Chelsea at just 8 years old.
The England international was offered a two-year deal with an option for an extra year but the midfielder rejected the deal due to the length of the contract and the role offered which was less significant than the one he currently has.
New Chelsea boss Enzo Maresca has a possession-based style of play which many believe does not suit Gallagher and that it the main reason there was such a divide between him and the club.
The move to Atletico was favoured over a domestic move and Gallagher becomes one of the only Englishman to enter La Liga which includes the likes of Jude Bellingham.