The Bosnia international, who joined from Ferencvaros for £4.8million in the summer of 2014, has been rewarded for some impressive displays this season.
Besic had already this season triggered a clause in his existing contract which entitled him to a 12-month extension by reaching 25 Barclays Premier 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 per cent stake in the Toffees for a reported £85million.
Utility man Bryan Oviedo signed a new contract earlier this month while Everton are also hopeful of tying down Ross Barkley to an improved deal this summer.
"I'm really happy to have signed a new contract with a club such as Everton," Besic told evertontv.
"After a year and a half with the club it makes me proud that they have given me a new deal."
"When I first arrived here it was difficult for me but now I feel at home. The supporters, as well as the manager, the staff and my team-mates, have all made me welcome at the club and I feel really happy.
"It was very easy when I heard about it. It was clear that I wanted to stay and sign the new contract.
"When people look at my game, before and now, I think I have improved a lot in many different areas.
"But I am still adapting to the league and I will continue to work hard and give my best."
Source: PA