The Colombian is currently one of the most in-demand forwards in Europe having struck 27 goals in 61 games for the club since joining from Club Brugge in 2013.
The 28-year-old has also started this season in fine form, netting six times in nine games in all competitions.
"I thank God that we did some great work last season and I have the confidence of the coaching staff, the directors, and all the supporters," he told El Heraldo.
"I'm very happy to be a part of this team that has given me so much joy. It has made me grow as a player and also a human being.
"I feel as though I'm doing very well, working with humility and a desire to keep on improving, and I'll continue to give my best for Sevilla and my national team."
Arsenal were strongly linked with the forward in the summer.