Gallagher, who had been at Chelsea since the age of eight, has signed a contract until 2029 with Atletico who have paid 42 million euros (£36m) for the 24-year-old, according to media reports.
"We wish Conor the very best as he begins a new chapter in his career," Chelsea said in an official announcement published on their website.
Gallagher spent the early part of his senior career on loan, including spells at Premier League clubs West Bromwich Albion and Crystal Palace, and did not make his Chelsea debut until 2022.
Last season Gallagher started 37 Premier League games, missing just one league match through suspension, and spent most of the campaign as club captain due to injuries to Reece James and Ben Chilwell.
Gallagher had one year left on his Chelsea contract, and new manager Enzo Maresca recently stated that he had been offered a new contract.
He made his England debut in 2021, has 18 caps and made five appearances at Euro 2024 where England reached the final, losing 2-1 to Spain.
Gallagher and Atletico's other new signings will be unveiled later on Wednesday in a party open to fans at their Metropolitano stadium, headlined by former Manchester City forward Julian Alvarez.
Atletico have now spent around 200 million euros following deals for Spain defender Robin Le Normand and Norway striker Alexander Sorloth.
After a disappointing 2-2 draw at Villarreal to start the La Liga season on Monday, Atletico host last year's surprise package Girona on Sunday.
