The 24-year-old, who represented England at this summer's European Championship, has been with Chelsea since 2008, progressing through the youth system before making his first-team debut in 2019.
Gallagher was a vital player for the Blues during the 2023-24 campaign, scoring seven goals and registering nine assists in 50 appearances in all competitions, including five goals and seven assists in the Premier League.
However, there has been huge speculation surrounding the future of the midfielder in recent months.
Gallagher's contract at Stamford Bridge is due to expire next summer, and any sale during the current window would count as pure profit under the Premier League's Profit and Sustainability rules.
Atletico confirm Gallagher deal is imminent
Atletico have now posted a picture of Gallagher on their official X account showing the midfielder at Wanda Metropolitano, with a move on the verge of being completed.
According to transfer expert Fabrizio Romano, the midfielder has signed a contract with Diego Simeone's side until the summer of 2029.
Atletico are expected to pay in the region of £33m for the midfielder, who had allegedly been offered a new two-year contract by Chelsea with the option of a further 12 months.
However, according to BBC Sport, Gallagher had been informed that he would not be a key player for the Blues next season under the management of new head coach Enzo Maresca.
Is Gallagher a good signing for Atletico?
Gallagher's high-energy style makes him the ideal midfielder to operate in Simeone's system at Atletico, and he also demonstrated last season that he can both score and provide assists at the top level.
Maresca's possession-based ideas at Chelsea could have made it difficult for Gallagher to secure regular starts next term, which would have been difficult for him to take after impressing last term.
Atletico play a different style, though, and Gallagher could be absolutely vital for the Red and Whites, especially in big matches away from home in both La Liga and the Champions League.
The England international is set to leave Chelsea with a record of 10 goals and 10 assists in 95 appearances, and he is now preparing to sample life in another major European league.