The fee for the 24-year-old Portugal international is undisclosed, but it will allow him to return to Stamford Bridge on a six-year deal with an option for a further season.
Felix’s move, which is subject to a medical, will bring him back after a 2023 loan spell at Chelsea.
He scored four goals in 20 appearances in his previous spell in west London.
England midfielder Gallagher, meanwhile, is set to sign a five-year deal with Atletico.
He had been training alone at the club’s Cobham training ground after being left in limbo for a week.
The collapse of Chelsea’s talks to sign striker Samu Omorodion had delayed Gallagher’s £33m move to Madrid, with Atleti needing to raise funds to complete the move by making a major first-team sale.
Chelsea will focus on player sales in the lead up deadline day on 30 August but remain interested in Napoli striker Victor Osimhen, as the Italian club continue their efforts to sign Romelu Lukaku, who remains on Chelsea’s books but has no future in west London.
Felix’s move to Chelsea will pave the way for Gallagher to sign on at Wanda Metropolitano Stadium, where he was pictured at nine days ago in anticipation of a move before a delay forced him to fly back to London last Tuesday.
