Midfielder Miguel Pallardo has signed a new one-year deal with newly-promoted Hearts.
Liam Rosenior has thanked the fans of Hull City for "five wonderful years".
The Northern Irishman ended his first season in charge of the McDiarmid side by leading them to their first ever major trophy with May's William Hill Scottish Cup triumph.
The 50-year-old was entering the final year of his contract but his new deal will tie him to Saints until 2017.
Wright - who replaced compatriot Steve Lomas last year - told the club's official website: "I'm delighted to sign a new contract. I've always said that I see my future being at St Johnstone and from the end of last season the chairman and board made it clear to me that they were more than happy for me to continue.
"I have a good relationship with everyone at the club - the board, the staff, the players and supporters. I'm privileged to manage a club like St Johnstone.
"There was never any question that it wouldn't be extended but sometimes people don't realise it doesn't happen overnight. What with the Europa League and a busy pre-season schedule and the fact that my mum was ill and unfortunately passed away, other things of more importance took priority.
"However, it's now done and dusted and I'm looking forward to continuing to work with the players and try to bring more success to the club. Bringing more young players through into the first team is also a priority."
Chairman Steve Brown added: "Tommy has a great relationship with myself and the board and I'm looking forward to that continuing as we endeavour to develop the whole football structure from our youth academy to our first team.
"Continuity is important to us and it's great to have him secured until 2017 and everyone at the club is determined to continue to work together to endeavour to sustain the success of recent seasons."