The 25-year-old has been pulling up trees since he linked up with the Championship club in January until the end of the season and has become integral to their side already.
He has quickly become a mainstay in the heart of their midfield and helped Boro climb up to sixth in the league table as they try to secure a play-off spot.
Besic is due to return to the Goodison Park in the summer and should be kept in the first team ahead of the next campaign.
The Bosnia international is a no-nonsense defensive midfielder that is renowned for his tough tackling.
He can play a brilliant covering role in front of the back four, but is also very composed in possession and can help build up attacks from the back.
Besic was rightfully sent out on loan in January to experience regular first-team football as his time with the Merseyside club has been plagued by injury.
However, he showed in the past that he can be a very useful player in the Premier League and at 25 should soon be entering his peak years.
Idrissa Gueye is the first-choice midfielder in the Everton side as it stands, but there is certainly room to add Besic to the mix and he could compete alongside the likes of Tom Davies, Morgan Schneiderlin and James McCarthy next season.