France international Fekir, 26, entered the final 12 months of his deal at the start of July and LaLiga club Betis swooped to complete a transfer that could cost them €29.75million, with the deal also including a potential 20 per cent sell-on bonus for Lyon.
His younger brother, Yassin Fekir, has also moved to the Benito Villamarin, and Lyon will receive 50 per cent of any future transfer fee for the 22-year-old.
The versatile attacker, who has hit 36 Ligue 1 goals in the last three years, almost moved to Liverpool in 2018 and was linked to Arsenal after declining to discuss new terms with Lyon, the club he captained for two seasons.
Fekir progressed through the Ligue 1 side's academy and helped France win the World Cup in Russia last year.
His arrival in Seville is expected to free up midfielder and fellow left-footer Lo Celso for a switch to Tottenham.
A full Argentina international, the 23-year-old is reportedly keen to work with compatriot Mauricio Pochettino in London.
Lo Celso joined Betis on loan from Paris Saint-Germain at the start of last season, before the move was made permanent in April.
Tottenham will reportedly have to spend around €75m to make him their third close-season signing after Lyon midfielder Tanguy Ndombele and Jack Clarke, who has returned to Leeds United on loan.