Hogg returns to captain the side after joining second row Gray and Wales prop Tomas Francis in the Exeter Chiefs side that added the English Premiership title to the Heineken Champions Cup they won the previous weekend.
They are two of five changes from the side that beat Georgia 48-7 at Murrayfield last Friday night.
The other changes see Russell selected at outside-half to win his 51st cap while Ali Price comes in at scrum-half to join him.
Blair Kinghorn shifts to the wing from full-back and replaces Edinburgh teammate Duhan van de Merwe, who is named among the replacements.
Up front, Scarlets No 8 Blade Thomson gets a back-row berth which means he will face Wales on his home pitch in Llanelli.
The marauding Hamish Watson and Jamie Ritchie join Thomson in the back-row with Scott Cummings packing down with Gray in the second row. Fraser Brown has been named as vice-captain and will be in the middle of an unchanged front row alongside Rory Sutherland and Zander Fagerson.
Former RGC 1404 outside half James Lang, now playing his rugby at Harlequins, lines-up alongside and Chris Harris in the centre.
“As a group we are very much looking forward to finally completing our fixture against Wales and returning to play Guinness Six Nations rugby again. We were highly motivated back in March and that extra edge has come back into our training and preparations this week, said Scottish coach Gregor Townsend.
“It’s great to be able to bring in quality and experience to our starting line-up with players such as Stuart, Jonny and Finn who have been involved in some high-level games in recent weeks. We were also encouraged by Blade’s display at the weekend for Scarlets which is a timely boost given last weekend’s injury to Matt Fagerson.
“We are expecting a physical battle against a very good side. We will be working hard to stay in the fight and to finish the fight in Llanelli.
“Ultimately, this game provides an opportunity for us to end this extended championship on a positive note and go into the Autumn Nations Cup with some added belief in what this group of players can achieve.”
The Scottish line-up shows seven changes from the starting XV selected to play in the original game in Cardiff in March while Wayne Pivac’s Wales team has 10 changes.
15. Stuart Hogg (Exeter Chiefs, CAPTAIN) 76 caps
14. Darcy Graham (Edinburgh) 12 caps
13. Chris Harris (Gloucester) 19 caps
12. James Lang (Harlequins) 3 caps
11. Blair Kinghorn (Edinburgh) 22 caps
10. Finn Russell (Racing 92) 50 caps
9. Ali Price (Glasgow Warriors) 33 caps
1. Rory Sutherland (Edinburgh) 8 caps
2. Fraser Brown (Glasgow Warriors) 51 caps
3. Zander Fagerson (Glasgow Warriors) 30 caps
4. Scott Cummings (Glasgow Warriors) 13 caps
5. Jonny Gray (Exeter Chiefs) 57 caps
6. Jamie Ritchie (Edinburgh) 19 caps
7. Hamish Watson (Edinburgh) 33 caps
8. Blade Thomson (Scarlets) 5 caps
16. Stuart McInally (Edinburgh) 38 caps
17. Oli Kebble (Glasgow Warriors) 1 cap
18. Simon Berghan (Edinburgh) 26 caps
19. Ben Toolis (Edinburgh) 26 caps
20. Cornell du Preez (Worcester Warriors) 8 caps
21. Scott Steele (Harlequins) Uncapped
22. Adam Hastings (Glasgow Warriors) 21 caps
23. Duhan van der Merwe (Edinburgh) 1 cap