The 25-year-old, who is currently with Worcester Warriors, has made one international appearance for England.
"I have had a great eight years at Worcester and leaving your home town club is always hard. However I felt the time was right for a new challenge and I am looking forward to joining up with London Wasps next season," he told Sky Sports News.
"As a club with lots of other aspiring young English players, I hope to be part of a successful side there in the coming years."
Meanwhile, Wasps director of rugby Dai Young added: "Matt's achieved plenty in his career to date but I believe there is a lot more to come from him.
"He will add to our growing base of young English talent at London Wasps and we're pleased he will be with us from next season."
Mullan toured with the England squad in South Africa last summer.