Sevilla president Jose Maria del Nido insisted earlier this week that his club had not received any offer from Manchester City for 27-year-old Negredo, who has indicated he would like to leave the Andalusian club this summer.
Bacca has agreed a five-year contract with Sevilla and has a 30million euros release clause in his contract, the club announced on their official website.
The deal was sealed after Sevilla's sporting director Ramon Rodriguez, known as Monchi, travelled to Manchester to finalise terms with the player, who is on a pre-season tour with Club Brugge.
Neither Brugge nor Sevilla have confirmed the fee, which is reported to be around 7million euros.
The move will put City and Tottenham on the alert as the Colombia international appears to have been bought as a replacement for Negredo.
City have emerged as the favourites to sign the striker, who was the highest-scoring Spaniard in La Liga last term with 25 goals.
Source: Manchester City MAD