Scrum-half Scott Steele has also been recalled by his club, Leicester, with Matty Torrance starting at scrum-half in his place.
Despite losing 28-15 to Wales last time out the two enforced changes are the only alterations Wright has made to his side and the head coach hoping his faith will be rewarded.
"Both Tommy and Scott getting recalled to their clubs means Finn Russell comes in at 12 and Matty Torrance starts at scrum-half," he said.
"Finn is probably more of a 10 but bringing him in for Tommy means it's a bit more like for like and I'm excited to see what he can do at inside-centre from the start.
"Scott Steele has gone back to Leicester, a good opportunity for him to experience the Premiership set up, but Matt brings in some pace and his delivery is quick and accurate.
"What we've got to do is get a bit more accurate especially around the contact areas and tackles.
"We made 94% of tackles against Wales but in that 6% we missed, we conceded two tries."
15. Sam Hidalgo-Clyne (Scotland 7s/Heriot's)
14. Jamie Farndale (Edinburgh Rugby/Edinburgh Accies)
13. Robbie Fergusson (Ayr)
12. Finn Russell (Falkirk)
11. Michael Crawley (Boroughmuir)
10. Harry Leonard (Edinburgh Rugby)
9. Matt Torrance (Ospreys)
1. Jamie Bhatti (Stirling County)
2. George Turner (Edinburgh Rugby/Stewart's Melville)
3. Alex Allan (Loughborough Students)
4. Adam Sinclair (Stirling County)
5. Jonny Gray (Hamilton)
6. Mitch Eadie (Bristol Rugby)
7. Will Bordill (Sale Sharks)
8. Jamie Swanson (Boroughmuir)
16.Fergus Scott (Currie)
17.Gavin Robertson (Dundee HSFP)
18.Andrew Redmayne (Dundee HSFP)
19.Callum Reid (Edinburgh Accies)
20.Callum Maguire (Berwick)
21.Murray McConnell (Glasgow Warriors)
22.Jack Bradford (Nottingham)
23.Tom Steven (Glasgow Hawks)