The transfer is worth around €4m, with Real Madrid retaining 50% of any future sale.
It becomes Manuel Pellegrini's second signing of the summer following Uruguayan full-back Facundo Bernal, and addresses a position that has troubled Real Betis since Alex Moreno's departure, with the fee kept low enough not to disrupt the club's tight wage structure as they prepare for Champions League football.
Garcia flew into Seville on the morning of the announcement and was due to join his new team-mates in Germany the following day for the first stage of pre-season training. The move became increasingly logical for Madrid given Garcia had a year left on his contract and faced growing competition following Marc Cucurella's arrival at the club.
An academy product who joined Real Madrid's youth ranks as a 14-year-old cadet in 2013, Garcia first broke into the first team in a Copa del Rey tie against Melilla at the Santiago Bernabeu in December 2018 - the same match in which Alvaro Fidalgo, now his new Betis team-mate, also debuted.
He left for Rayo Vallecano in 2020, making 122 appearances and scoring five goals there, before Madrid brought him back in 2023. Across three seasons back at the club he made 110 appearances, winning five trophies: the Champions League, Club World Cup, European Super Cup, La Liga and Spanish Super Cup.
Garcia marked his departure with a personal letter posted on social media rather than a formal club statement.
"The time has come to say goodbye to one of the most beautiful stages of my life," he wrote, dating his story back to the 11-year-old boy who first walked into the club's Valdebebas training ground.
He thanked president Florentino Perez and José Angel Sanchez for the chance to fulfil a childhood dream, along with coaches, medical staff, kit workers and cleaning staff at the club.
"You instilled values in me that I will always carry with me, especially never giving up and fighting until the end," he wrote.
"And that is what I have done for this shirt, fighting until the end from the first day I wore it to the last. I have won important titles with the club, but the biggest of all is the affection of every Madridista.
"I will always carry you in my heart. Thank you for everything, and see you soon."