The former England number 10, who moved to Worcester in 2010, will head to his new club in second place of the all-time Aviva Premiership points chart.
"I am delighted to be joining London Wasps next season and it is clear they have made some big strides forward this year and are clearly heading in the right direction," Goode told the club's official website. "At the same time, I'm committed to doing my best for Worcester Warriors until the end of the season."
Director of rugby Dai Young added: "The Aviva Premiership is an incredibly tight league and there are more one score games in this league than any other, so it is vitally important to have a recognised goal kicker in your squad.
"Andy's record in the game speaks for itself and tactically he is an excellent number 10 and I am confident he will also get our backline moving very well."
Goode won 17 caps for England and racked up 107 points.