The 29-year-old, who has 16 caps for his country, started his career at Leeds before joining Wasps and then moving on to The Rec in 2012.
He will cover the loss of Sale hooker Tommy Taylor, who has agreed a move to Premiership rivals Wasps.
Webber was part of England's World Cup squad in the summer, but was not picked for the forthcoming Six Nations.
"Rob fits perfectly into what we are trying to create at the club. He is a talented all round player, who is great at the set-piece and very mobile in the loose," said Sharks director of rugby Steve Diamond.
"He is at the top of his game and will bring with him a wealth of experience."
Webber has made 59 appearances for Bath, and scored seven tries.
"I'm really looking forward to the new challenge ahead. I have spoken to Steve Diamond and the lads I know at the club and they have all spoken highly about the environment at Sharks and what the club are looking to achieve," he said.
Sale Sharks have completed a deal to sign Bath and England hooker Rob Webber on a two-year deal from next season.