The Italian international, who joined the Chiefs in the summer of 2015 from Benetton Treviso, became a free agent.
Wasps had been heavily tipped to sign him and the club have confirmed the signing of the Italy international.
The centre, who will link up with his new teammates after the Autumn Internationals, has signed a deal until the end of the season.
The 25-year-old has 36 international caps to his name and played in every game for Italy at the 2015 Rugby World Cup.
He has also scored nine international tries, including two in the last fortnight which have come against Ireland and Georgia.
Following the last Rugby World Cup, Campagnaro made the switch to Exeter, making his debut in November 2015, before going on to bag nine tries in 27 appearances for the Chiefs.
During his time at Sandy Park he was part of the squad which reached the Premiership final in each of the past two seasons, winning it in 2017, and also the Anglo-Welsh Cup final in both seasons, winning it earlier this year.
Campagnaro previously spent three years at Treviso where he made 34 appearances, having crossed the whitewash six times.
Wasps Director of Rugby Dai Young said: “Michele is an experienced international who predominantly plays at 13, but having also played on the wing and at 15, his versatility will be of huge benefit to the team throughout the season.
“He joins us with some real pedigree and we’re looking forward to integrating him into the squad.”
Campagnaro said: “The opportunity to join Wasps was something no player can turn down.
“Wasps play an exciting brand of rugby and have a number of talented individuals. I’m very much looking forward to testing myself and playing at the Ricoh Arena.”
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