The 28-year-old centre made 125 appearances for Bath Rugby, scoring 21 tries, and was appointed joint captain for the 2008/09 season.
Crockett, who has previously played for his country at Under-21 level, was called into the England Saxons squad to face Italy A in Ragusa, Sicily in February 2008.
He joined Bristol on a short-term deal in January and will now move to Warriors for the start of next season.
Richard Hill Worcester Warriors Head Coach commented: "I am delighted that Alex Crockett will be joining us at the beginning of the season. He brings great leadership qualities which made him Captain at Bath Rugby."
"I have known Alex for a long time have followed his career, from a very young age he showed great talent. He is a very talented intelligent rugby player which will be a great asset to the club."
"Now that Alex Grove has gone on loan to pursue his international career it will be a great compliment to Alex Grove and will no doubt help him long term."
"I feel we have great quality in midfield with players who can both contribute in attack, defence and with the leadership of the team."
When commenting on the announcement Crockett stated, "I am thrilled about the opportunity that lies ahead at Sixways with the Worcester Warriors, this is an exiting time for myself and the club. I am looking forward to working with my new team mates and coaching staff and getting the Warriors back where they belong."
Crockett added "I cant wait to get started at the club and start moving forward as a new group with the right structures in place on and off the field"