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 entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
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.