The 25-year-old forward has spent six years with Wasps following his arrival from Leeds Tykes in 2005 and has made 107 appearances for the club.
Webber has regularly been called upon to captain Wasps while developing his own game to the level which saw him earn an England U21 call-up, before graduating to the England Elite Player Squad.
Webber admitted that the decision to leave Adams Park was a difficult one but vowed to continue performing to the best of his ability for the remainder of the season.
"It was a very tough decision to move on as I have loved my time as a Wasps player," he told the club's official site.
"I arrived down to London from Leeds as a teenager and in my time here I have learned a lot about both rugby and life and the friends I have made I would consider to be friends for life.
"I will continue to give my all for the rest of the season and I know I will always be a fan of the Club no matter where I go next."
Webber made his debut for the Wasps against Saracens before going on to score three tries for the club and his on and off field qualities will be missed.
"We will be sad to say goodbye to Rob because he's been a key player for the club developing into one of the senior voices in the squad," Wasps director Dai Young added.
"We were hoping to hold onto him and we made him a much improved contract offer but these decisions are up to the player at the end of the day.
"He goes with our very best wishes and I know he will give it his all in a Wasps shirt for the rest of the season."
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.
