Gabi, a product of Atletico's youth set-up, spent 11 seasons at the club across two spells, winning one La Liga title and two UEFA Europa Leagues among six trophies, and will link up with former Barcelona talisman Xavi Hernandez with the option of a further 12 months.
"This is a difficult and emotional day for me," the 34-year-old midfielder told a news conference at Atletico's Wanda Metropolitano stadium.
"It's been the hardest moment of my career. This club is a lifestyle for me."
Gabi made 417 appearances for Atletico and also played for La Liga rivals Getafe for one season on loan and Real Zaragoza from 2007-11 before returning to the Spanish capital.