Lomas quit the Perth outfit last week to take over at Championship side Millwall and he will be succeeded at McDiarmid Park by his former assistant Wright.
Saints chairman Steve Brown has also announced that current first-team defender Callum Davidson will assist the new man in charge.
Wright is currently on a family holiday but will be unveiled at a press conference on Tuesday, June 18.
A statement issued by Saints stated: "The club is delighted to announce the appointment of Tommy Wright as the new manager of St Johnstone Football Club.
"Tommy is joined by Callum Davidson, who will work alongside him as his assistant.
"The club welcomes this exciting new chapter, heralding the start of a challenging European and domestic campaign."
Wright started his coaching career as a goalkeeping specialist under Glenn Roeder at Norwich but made his move into management with Limavady United in his homeland in November 2003.
Spells in charge of Ballymena United and Lisburn Distillery - where he led the Whites to the Irish League Cup in 2011 - followed before he made the move to Scotland to work alongside his former international team-mate Lomas.
- Sports & Recreation
- Callum Davidson