The Premiership side have been playing their home games at Wycombe Wanderers' Adams Park, but have long been seeking a permanent home ground.
A deal to purchase Coventry City Council's shares in Arena Coventry Limited (ACL) was unanimously backed by councillors on Wednesday and the agreement has now been formally announced.
"This is a watershed moment in the history of Wasps and the professional game," said Wasps chief executive Nick Eastwood.
"It will help us realise our ambition to re-establish ourselves as one of the best teams in Europe and will guarantee the long-term success of the club."
Wasps' decision to move away from the London area has caused anger among the club's fans, but Eastwood reiterated that serious thought has been put into the switch.
"We fully appreciate this move will unsettle many of our supporters and I would like to stress that this decision has not been taken lightly," he added.
Eastwood also insisted that football club Coventry City, who moved back to the Ricoh Arena in August following a long dispute with ACL over rent, would not be forced out as a result of the deal.
In addition, Eastwood stressed that the club's name would be Wasps and not Coventry Wasps.
"We want Coventry City playing alongside us," he said.
"Our experience in ground-sharing has proved successful and we are aware the Sky Blues fans and players have experienced uncertain times.
"We are delighted for them to be back at the Ricoh, though. We want a long and successful relationship with them.
"We will not be Coventry Wasps. We will be Wasps."
Wasps' first game at the Ricoh will either be against Castres in the European Champions Cup on December 13 or in the Premiership versus London Irish eight days later.