Besic has been rewarded for some impressive displays since moving to Goodison Park from Hungarian outfit Ferencvaros in 2014.
The Bosnia international had already this season triggered a clause in his existing contract which entitled him to a 12-month extension by reaching 25 league appearances for the club, but Everton manager Roberto Martinez was keen to tie the player down to a much longer term.
It is more good news for the club in the wake of the weekend's investment by Iranian billionaire Farhad Moshiri, who bought a 49.9 percent stake in the Toffees.
"I'm really happy to have signed a new contract with a club such as Everton," Besic told the club's website.
"After a year and a half with the club it makes me proud that they have given me a new deal."