The Bosnian arrived at Goodison Park last summer on a free transfer, putting pen-to-paper on an initial one-year deal.
Begovic has played the role of deputy to Toffees number 1 Jordan Pickford this season, with the majority of his minutes coming in cup games.
The 34-year-old has made two appearances in the Premier League so far this season, and he kept a clean sheet in one of them.
Begovic’s current deal at Goodison Park includes an option to extend his stint by a further season, which Everton have now taken up.
Toffees boss Frank Lampard has been pleased with how Begovic has stepped up for the team when called up on, and wants him to remain at the club beyond the current campaign.
While Everton have sorted out Begovic’s contract situation, their own future in the Premier League remains up in the air.
It has been claimed that Pickford will push to leave Goodison Park in the summer if they slip down to the Championship.
