The 25-year-old, who started his professional career in the Leeds Carnegie Academy before moving to Wasps, is strong in the set-piece, and extremely mobile and athletic in the loose.
Webber will still be available for the knockout stages of the Amlin Challenge Cup with Wasps set to meet Heineken Cup qualifiers, Biarritz, in what promises to be a high-quality quarter-final at Adams Park on Saturday, 7 April.
He has represented England at all age group levels, from Under 16s to touring with the Saxons in 2010, and will be looking to gain his first full cap during the upcoming 6 Nations.
Speaking of the signing, Director of Rugby, Sir Ian McGeechan, said: "Rob is a very skilful and exciting player. He has a great work ethic and attitude, comes to us with an already impressive skill-set, and still has a lot more potential. We are looking forward to helping him develop his game further, and feel he will fit in very well here at Bath."
Webber added: "I have loved my time at Wasps, but it is time to move on, and I am genuinely excited at the prospect of working with the squad and coaches at Bath. There seems to be a great ethos developing at the club, both on and off the field, and it's one I'm looking forward to becoming part of."