The midfielder, a five-time UEFA Champions League winner who made 353 appearances during a nine-year spell with Los Blancos, fell out of favour following Carlo Ancelotti's return to the Santiago Bernabeu last year.
He left the Spanish capital following the expiration of his contract in June, having made just three starts during Madrid's double-winning 2021-2022 campaign, playing just 406 minutes in all competitions.
Sevilla swooped to sign the 30-year-old on a free transfer on Monday, and Isco hopes the move will revitalise his career.
"I want to show the level that I have and that I have never lost. It's normal for there to be doubts, but I'll take care of dispelling them," he told the club's media channels after signing a two-year deal.
"It has been a difficult summer, different. I've had too many vacations, I've taken advantage of them to get in shape and now I can't wait to play again, which I haven't done for a while.
"I'm not complaining, I've been lucky because I've played for big clubs and I've won almost everything, but I don't like to think too much about the past but about what's to come."
Isco's arrival in Seville will see him reunited with a familiar face in Julen Lopetegui, who coached him at Madrid in 2018 and during a spell as Spain boss between 2016 and 2018.
And the playmaker is excited to work with him at the Estadio Ramon Sanchez Pizjuan, adding: "He has always trusted me and I like his football, what he proposes. It is a football that is more suitable for my style.
"I thank him for his confidence, which for a footballer is paramount. The confidence he has given me, it has always been the maximum. Now it's up to me to restore his confidence on the pitch and show him that he's not wrong."
Isco could make his Sevilla debut when it begins its LaLiga campaign at Osasuna on Saturday AEST.