The 26-year-old striker has agreed a five-year contract with the Primera Division outfit and is set to be officially unveiled by his new club on Thursday evening.
No fee has been announced but reports in Spain suggest he could cost up to 10 million euros.
A statement on Sevilla's website confirmed Gameiro's contract will have a buy-out clause of 40million euros, adding: "Gameiro will be presented this evening at 2030 (local time) at the Sanchez Pizjuan, where the fans will be able to see him in the Sevilla shirt for the first time."
Gameiro played for Strasbourg and Lorient before joining PSG in 2011. In two seasons at the Parc des Princes, the Senlis-born hitman scored 23 goals in 77 competitive matches. He has also made eight appearances for France.
Gameiro will help cover the loss of striker Alvaro Negredo at the Ramon Sanchez Pizjuan, with the Spain international last week joining Manchester City after four years at Sevilla.