The 23-year-old defender - who spent three years in England at Bolton - will make Perth his third A-League club after stints at Adelaide United and the Sky Blues.
The signing of the left-back was just the latest in a line of youthful acquisitions by Glory coach Ian Ferguson, with Adrian Zahra, 21, and Chris Harold, 19, also joining the club from the Melbourne Heart and Gold Coast United respectively.
Ndumba Makeche, 20, and 18-year-old Brandon O'Neill also signed full-time contracts after impressing in the club's National Youth League team.
"Scott is a player I have admired over the years," Glory boss Ferguson said.
"He's a great addition to our squad and will make us stronger. We were very keen to add youth to our squad and it's great we've now added five players under 23 who have A-League experience.
"The signature of Jamieson is a coup for Perth Glory."
Jamieson, who has represented Australia on two occasions, is looking forward to linking up with a Glory squad who finished runners-up in the 2011-12 A-League season.
"I'm very excited to be heading to Perth," Jamieson said.
"I am extremely grateful for the opportunity and would like to thank Ian Ferguson. From the first time I had contact with Perth Glory, it felt like a good fit.
"Now I'm looking forward to playing with a group of talented players and developing my game with an astute coaching staff."