During his time at the Pilgrims, he also enjoyed loan spells at Weymouth and Exeter City.
Trollope added: "He is someone we have been looking at for a good 18 months.
"He's a player who will add to our defensive strength as he's an excellent defender, good in one-on-one situations.
"In addition, he's a six-footer and brings a versatility to the squad, as he can also play as a left-sided central defender.
"He can pass the ball well and likes to get forward and we feel that his signing is a big coup for the club."
Sawyer is Rovers' fourth summer signing, following the arrival of Harry Pell (Charlton), Wayne Brown (Fulham) and Will Hoskins (Watford) to the Memorial Stadium.
Trollope told BBC Radio Bristol: "We're in discussions with other players and are still hoping to close one before the end of the week.
"Ideally we still want three more and we're confident of doing that though it might take a week or two more.
"We're trying to build and progress to a sustainable Championship football club. The recruitment so far this year will help us in that quest."
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