Price was impressive in his most recent outing in Lions colours, maintaining a high tempo throughout Saturday's clash with the Stormers to help steer his side to a 49-3 victory.
Price is set to become the first Warrior to earn a Test cap for the British and Irish Lions since 2013, when Richie Gray came off the bench in the series-clinching third Test victory over Australia.
The number nine is one of five Scottish players selected by Gatland and his coaching team, with Duhan van der Merwe, Rory Sutherland, Hamish Watson and former Warrior Stuart Hogg joining Price in the matchday 23.
British & Irish Lions
15 Stuart Hogg (Exeter, Scotland)
1 Wyn Jones (Scarlets, Wales)
2 Luke Cowan-Dickie (Exeter, England)
3 Tadhg Furlong (Leinster Rugby, Ireland)
4 Maro Itoje (Saracens, England)
5 Alun Wyn Jones (C) (Ospreys, Wales)
6 Courtney Lawes (Northampton Saints, England)
7 Tom Curry (Sale Sharks, England)
8 Jack Conan (Leinster Rugby, Ireland)
16 Ken Owens (Scarlets, Wales)
17 Rory Sutherland (Worcester Warriors, Scotland)
18 Kyle Sinckler (Bristol Bears, England)
19 Tadhg Beirne (Munster Rugby, Ireland)
20 Hamish Watson (Edinburgh Rugby, Scotland)
21 Conor Murray (Munster Rugby, Ireland)
22 Owen Farrell (Saracens, England)
23 Liam Williams (Scarlets, Wales)