The Terriers removed assistant Steve Taylor, head of performance Darren Robinson and goalkeeping coach Paul Critchon from their positions last month as they looked to freshen things up following a disappointing second half of the season in the Sky Bet Championship.
Thompson, who had a lengthy spell at Blackpool and was number two to Ian Holloway when they won promotion to the Premier League, has been installed as Robins' deputy while Nick Colgan has been promoted to head of goalkeeping.
Allan Stewart has been appointed head of sports science and Dan Hughes becomes first-team strength and conditioning coach.
Boss Robins told the club's official website: "I am delighted that our new coaching team is taking shape well in advance of pre-season.
"As a group we have plenty of time over the next month to develop our working relationships and build rapport ahead of the players returning for the new season.
"A lot of work has been put into this process. I have personally met and talked to a lot of interesting and good people and the club is clearly one that is attractive.
"I am really excited by what each individual will bring to the players and the coaching and support set-up; it is a fresh beginning.
"We will work hard to improve our winning mentality, strengthen team spirit and improve our coaching environment.
"There is still some more work to do though, with the appointment of a first team coach the next priority ahead of the new season, but I am pleased and excited with how things are shaping up."