The Spaniard, 41, took over at the Riverside Stadium in November 2013 and guided Boro to the Sky Bet Championship play-off final last season, where they lost to Norwich.
The former Real Madrid coach, who worked alongside Mourinho, had been linked with other jobs but decided instead to reaffirm his position with Boro.
Gibson told the Evening Gazette: "This is massive statement of the commitment Aitor has to this club
For me this is probably the most important signing we will make all summer
"We know that there has been interest in Aitor over the past year or so from clubs both here and abroad, and rightly so because he is a very, very good manager.
"When that speculation has arisen he has always been quick to say that he is happy here and working in the best place
Signing this new four-year deal underlines that quite clearly
"It gives us a lot of stability going into the new season and the coming years."
Gibson added: "Aitor is very happy here, his family is happy here and he is putting down roots
He is very quickly becoming a Teessider
"He made a big decision to come here to another country and out of his comfort zone, and has been overwhelmed by the welcome he has had from supporters and from people across the area
He has been touched.
"He understands the important role the team plays in the area and the passion people feel for Middlesbrough Football Club - and he shares that."
Middlesbrough signed former West Ham winger Stewart Downing in a £5million deal and have now received international clearance on the transfer of Uruguayan international striker Cristhian Stuani
Boro's campaign begins on Sunday with a trip to Preston
Source : PA
Source: PA