The French playmaker joins the LaLiga side on a four-year deal reported to be worth approximately €30m.
The contract runs through 2023, with Lyon saying the deal is worth €19.75 million, plus €10 million in incentives and includes a potential 20% sell-on bonus.
A product of the French club's academy, Nabil played nearly 200 professional matches, scoring 69 goals and registering 41 assists. He became club captain in 2017 before winning the World Cup with France in 2018.
Fekir, 26, had been heavily linked to a move to Liverpool last summer but that transfer fell through due to a knee injury.
Fekir's arrival in Seville could also have ramifications for Giovani Lo Celso's future; the Argentinian international midfielder has been heavily linked with a move to Tottenham Hotspur in recent weeks.