Eastmond, capped six times, previously played for St Helens and the England rugby league team before switching codes to join Bath in 2011.
The 27-year-old made 72 top-flight appearances for Bath, scoring 16 tries, including two last season.
"Kyle has already shown his international class and still has plenty of potential to fulfil," Wasps director of rugby Dai Young said.
Wasps have not disclosed the details of Eastmond's contract at the Ricoh Arena. He had agreed a new deal at Bath in January.
Eastmond, whose last international appearance for England came against South Africa in November 2014, becomes Wasps' 12th signing ahead of the 2016-17 season.
"Kyle is one of the most exciting centres in the Premiership," Young told the club website.
"We're really looking forward to adding his talents to an already impressive group of backs at the club."
Wasps have signed England centre Kyle Eastmond from Premiership rivals Bath.