Pyrgos played 147 times for the Warriors and won 27 Scotland caps during his time in Glasgow. He is the joint most capped Warriors scrum-half of all time along with Graeme Beveridge.
Gregor Townsend named the scrum-half a Glasgow co-captain ahead of the 2016/17 season after Vern Cotter had made him Scotland captain for the 2016 Summer Tour to Japan.
The former Loughborough University student started the 2015 PRO12 Final, scoring a try as Glasgow went on to lift the trophy for the first time.
He crossed the whitewash 15 times in his Glasgow career also kicking twelve conversions and five penalties.
Glasgow Warriors Head Coach Dave Rennie said: "We're disappointed to see Henry leave. He is a good man and a good player, but we understand that this is the best decision for him and his family and it also a positive move for Scottish Rugby.
"Henry was part of the group of players that brought real success to the Warriors for the first time. He was a real leader here and the club means an awful lot to him and I'm sure it always will.
"I wish him and Perrie all the best for the future."