Saints moved quickly to replace Lennon, who was told on Monday his contract would not be renewed, by promoting his assistant.
The club also confirmed that Gary Teale and Jim Goodwin would be player/coaches in the new set-up.
Former Scotland Under-21 manager Craig assisted Lennon in the final three seasons of his four-year reign.
The pair first met when Craig was on the coaching staff at Hibernian and Lennon was a young player at Easter Road.
The 63-year-old also had coaching spells with Aberdeen, Celtic and Newcastle and worked at Hibs again with John Collins, who he later succeeded in a brief spell as Charleroi manager.
A club statement read: "The board of directors of St Mirren Football Club are pleased to announce the appointment of Tommy Craig as manager of the football club.
"Tommy has asked Gary Teale and Jim Goodwin to take on the role of player/coaches to assist him. Both are delighted to be on board and we look forward to our new management team taking the club forward.
"The initial work for Tommy will be to re-sign the players who are out of contract that he wishes to see remain in his squad, together with the identification of signing targets throughout the summer and programme our pre-season plans.
"The remit from the board is to continue the foundations already in place at St Mirren, part of which is to encourage young players from our academy to develop within our club.
"Tommy Craig has a proven record in this area and together with Jim and Gary will work with our successful head of youth, David Longwell, to ensure our young players continue to progress from youth academy to the first-team squad.
"The supporters of the club have been magnificent in the support of this policy, we are sure they will wish Tommy, Jim and Gary every success."
Skipper Goodwin, 32, and 35-year-old former Scotland winger Teale were both brought to the club by Lennon in 2011.
Lennon led Saints to a League Cup win last season as well as two eighth-placed finishes in the top flight, their highest placing since 1989.