The 27-year-old, a former New Zealand Under-21 international, made his Crusaders debut in 2009 and also captains Tasman in the Air New Zealand Cup provincial competition.
He said: "This is a really exciting move for me. I am looking forward to a different challenge in England.
"It has been difficult to be behind such a great player as Richie McCaw, and my opportunities to start games for the Crusaders have obviously been less than I would have liked."
Wasps chief executive Chris Thomas added: "Jonathan has excellent leadership qualities, and having featured for a number of seasons in one of the best club sides in the world, he will bring a lot of top experience to the squad."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.