The collapse of Chelsea's talks to sign Atletico striker Samu Omorodion had delayed Gallagher's move to Spain, but the Felix deal frees up the required funds for Atletico to complete the transfer.

Gallagher spent five days in a hotel in Madrid earlier this month expecting a deal before flying back to London when the move stalled.

Gallagher had loan spells at Charlton, Swansea, West Brom, and Crystal Palace before breaking into the Chelsea first team at the start of the 2022-23 season.

He has won 18 England caps since making his debut in 2021 and was part of the Three Lions squads for the 2022 World Cup and Euro 2024.

Nizaar Kinsella, BBC Sport football news reporter

Conor Gallagher's exit will leave a bitter taste in the mouths of some match-going Chelsea supporters who adored him.

They held up a banner in the match against Tottenham, a club many thought he might join, in May in protest of his expected departure.

That exit has happened, but a crumb of comfort is that Chelsea have sold him outside the Premier League to Atletico Madrid in Spain, avoiding the kind of pain some fans still feel when watching Mason Mount line up for Manchester United.

Chelsea have also handled his departure well by putting together an emotive video package that highlights his bond with the club and wishing him well for the future on all their channels.

It reads and feels like a celebration of the career of the boyhood Chelsea fan, who has been with the club since the age of six, as he departs for Wanda Metropolitano.

It's a positive end to a strange transfer saga that saw Gallagher training alone at Cobham in limbo as the two clubs tried to pull off a bizarre swap deal.

Gallagher will again be able to focus on his football and could be a good fit for Diego Simeone's dogged, high energy and physical style of play.