The 29-times capped international has joined the Scottish capital club on a one-year contract after eight years with Warriors.
Pyrgos made 147 appearances for Glasgow after joining from Loughborough University but only five of his 22 appearances last season were from the start amid competition from the likes of George Horne, Niko Matawalu and Ali Price for the number nine jersey.
Edinburgh head coach Richard Cockerill said: “Henry is a proven leader and comes with bags of experience which will add real strength in depth to our scrum-half group.
“He’s a winner and has captained Scotland, so it’s great that he feels Edinburgh is a place where he can compete for further honours with both club and country.”
Pyrgos added: “I’m really excited by the opportunity to join Edinburgh.
“The club has a great playing squad and coaching team, so I’m looking forward to being part of it.
“I believe the club is a great place for me to continue to develop as a player.
“I’ve thoroughly enjoyed my eight years at Glasgow. Winning the league in 2015 was an incredible moment and one I’ll always remember.
“I’d especially like to thank all the players, management and fans for their support over the years.”
Source : HeraldScotland