The 14-cap England international has spent the last two years at the Ricoh Arena after rejoining from Sale Sharks in 2016.
Cipriani, previously with Wasps from 2006 to 2010, will bring down the curtain at the end of the campaign and is reportedly eyeing up a move to Japan.
"I will be sad to leave Wasps, but my job is far from finished and I can promise the fans my absolute all until the end of the season as we tackle the mission ahead of us," he told the club's official website. "I will now take some time to decide my next move."
Wasps director of rugby Dai Young added: "Danny is moving on at the end of the year and we wish him well. We would also like to thank him for all his efforts in a Wasps shirt.
"As he says, now this decision has been made public we can all concentrate on the really important three-and-a-half months of rugby which lies ahead.
"This begins for Danny, the rest of the squad and staff at the Ricoh on Sunday, where our focus is fully on the challenge presented by Exeter."
Cipriani has not featured for England since August 2015, with his 14 caps spanning over seven years.