The former St Johnstone boss has signed a contract until the summer of 2023 and will take charge of his first match against Motherwell at Rugby Park on Wednesday.
His arrival comes eight days after the departure of Alex Dyer, who was sacked after the 3-2 defeat at home to St Johnstone on Saturday, January 30.
Wright had been out of the game since quitting St Johnstone in May after seven years with the Perth club, which included guiding them to the first major honour in their history, with a Scottish Cup success in 2014.
The former Northern Ireland goalkeeper also led the Saints to five top six finishes and four Europa League qualifying campaigns during his tenure. His first task at Killie will be to arrest a five-game losing slump that has left them four points ahead of bottom club Hamilton.
“I’m absolutely delighted to be the new Kilmarnock manager. It’s a great opportunity for me,” Wright told the Kilmarnock website.
“I had nine years in total at St Johnstone and the time was right from me to leave there but it is the perfect time for me to come back to management.
“Kilmarnock has had good success in recent years and I’m looking to take it forward and moving us up the table.
“This is a really good football club with good people and I was really impressed when speaking to them, which made it an easy decision to take the job.”
Kilmarnock director Billy Bowie added that the club were “thrilled” to land Wright as their new boss.
He said: “We received a number of excellent applications but we believe Tommy is the right candidate to lead us up the Premiership table in the season’s remaining games while sharing our vision for the club’s future.
“He is an outstanding manager with a strong track record in this league of improving players whilst remaining committed to blooding young talent through the ranks.
“I’m sure our supporters will join me in welcoming Tommy to Killie and wishing him every success in his time at Rugby Park.”
Wright will be assisted by Paul Stephenson, who returns to Rugby Park having been part of Lee Clark’s coaching staff, with Andy Millen departing the club.