The prolific attacker completed a medical on Tuesday and has signed a five-year deal with the Primera Division outfit.
The Ramon Sanchez Pizjuan side were keen to add some more firepower to their squad and they saw the 26-year-old Bacca as the ideal signing.
|25/1||Sevilla are 25/1 with Coral to win the Europa League
"I had a fantastic time at Brugge and their fans will forever have a place in my heart. It makes me proud that I am the club's most expensive outgoing transfer ever."
Bacca, who scored 22 goals in 25 games in Belgium's top flight last season, becomes Sevilla's sixth signing of the summer after the previous capture of Raul Rusescu, Jairo, Víctor Machin, Marko Marin and Nico Pareja.
The arrival of the Colombian forward could open the door to a summer exit for Alvaro Negredo.
The 27-year-old is being heavily linked with a move to Manchester City and the Premier League giants could step up their interest in the Spain international in the upcoming days now Sevilla have signed a replacement.