It had already been announced the 30-year-old would leave the Warriors when his contract expires this summer.
The South Africa-born forward becomes Sale's first new signing for next season.
"Josh is a world class ball-carrying forward," said Sharks director of rugby Steve Diamond.
"He has been performing well for both Glasgow and Scotland over the past five years and will complement the squad in the ball-carrying department."
Strauss joined Glasgow from Super Rugby side Lions in 2012 and, after three years of residency, qualified to play for Scotland in time for the 2015 World Cup.
Number eight Strauss has been sidelined by a kidney injury sustained during the Six Nations defeat by France, ruling him out of the rest of the tournament.
"Since coming to the UK I always had it in the back of my mind that I wanted to play in the Premiership," said Strauss.
"I have really enjoyed my time with the Warriors, but I asked my agent to look around for me. He came back with Sale Sharks who have a good name, a good record in the Premiership and looked an attractive proposition."
Premiership side Sale Sharks will sign Scotland and Glasgow back row forward Josh Strauss on a three-year deal from next season.