Both will make the step up to full professional contracts from next season adding to Glasgow's list of successful BT Sport Academy graduates.
Flockhart returns to Scotland having spent last season on loan at French Federale 2 club, Stade Nicois.
The 20-year-old Number 8 had previously played for Glasgow Hawks in the Premiership and was also a member of the Scotland U20 squad that recorded a best-ever finish at a World Rugby U20 Championship in Georgia last summer.
Nairn joined the BT Sport Academy last season from English Premiership side Harlequins and featured in Glasgow's pre-season fixture against Northampton Saints at Bridgehaugh last year.
The winger travelled to two HSBC World Rugby Sevens Series tournaments with Scotland last season and was also a member of the Scotland U20 squad which finished fifth in Georgia.
Nairn could feature against his former side, Harlequins in The Famous Grouse Pre-Season Challenge in Perth on Saturday 18 August.
Flockhart and Nairn will join USA international David Tameilau in the Warriors squad next season, while DTH van der Merwe re-joined the club in March and George Turner made his loan move from Edinburgh permanent at the start of the year.
Speaking to glasgowwarriors.org, Bruce Flockhart, said: "Speaking to Dave (Rennie) he gave me an idea of what he's looking for from his back-row. One of the goals was for me to develop physically in France and, as a young player, French rugby has been perfect for me in that regard.
"My time in the BT Sport Academy, straight from school, has given me a taste of what professional rugby is about and was great for my development. Next season my goal is to learn as much as I can from the players around me and take my opportunities when they come."
Robbie Nairn said: "It's incredibly exciting to sign a professional deal with Glasgow Warriors. I've had a frustrating year, I had great fun playing for the Warriors in pre-season and was playing well before I got injured. I feel like I've shown bits of what I can do but I'm looking forward to getting into pre-season and giving a good account of myself in front of all of the coaches.
"I spent a lot of time in the Warriors environment last season and I learned the standards that are expected at this club. Dave's focus on basic skill levels has really helped me and there's always a lot of concise feedback. Developing a relationship with coaches is important for a young guy like myself and I'm going to try and learn as much as I can from them and my teammates too.
"Playing against Harlequins in pre-season this year will be a bit of a strange one. I'm focused on having a good pre-season and it would be good to get selected for that game and catch up with some old friends and hopefully get the win. I just want to give a good account of myself in the first few weeks of the new season and take it from there."