From 2017
Speaking ahead of Sunday's visit of Manchester United, Gibson told the club's official website,
www.mfc.co.uk: "Steve will have full autonomy as first-team coach. I hope he's here this time next year or the year after.
"He has a lot of qualities. He is a very good coach, a deep thinker, loads of experience, knows this club, is a man of integrity and the players trust and like him.
"I've known him a long, long time and he's a smashing lad. I think he can be the glue to unify us completely."
Agnew has little time in which to make an impact with Boro languishing inside the Premier League relegation zone, but Gibson is confident he has enough to work with.
He said: "I think the squad is good enough to stay up, but it has been a difficult period. Perhaps we are low on confidence and it's Steve's job to raise that."