The 24-year-old is due to arrive in the UK early next month and will be available for the first seven matches of the LV=Insurance County Championship season.
Worcestershire moved to sign Joseph due to ongoing fitness concerns over Josh Tongue and Pat Brown.
Paul Pridgeon, the club’s steering group chairman, explained: “Alzarri is a quality performer, and we are delighted to have signed him for the best part of two months.
“With it looking like Josh and Pat may not be match fit for the start of the season, Alex Gidman (head captain) and Joe Leach (captain) both felt they needed another seamer.
“Alzarri is going to be available for seven matches and is an exciting prospect.
“He opened the bowling in the Tests against England last year and more recently played in the ODI side against Sri Lanka.”
Joseph, part of the team currently playing Sri Lanka in the Caribbean, has taken 34 wickets in 14 Test appearances for the West Indies.
He has also developed into a useful performer with the bat, recently scoring 86 against New Zealand in Hamilton and 82 versus Bangladesh.
Worcestershire begin their County Championship campaign away at Essex on April 8.
He said: “I am thrilled to be joining Worcestershire for the early part of the summer.
“When I heard the club was interested in me, I had no hesitation in saying yes. The club has a strong squad with a nice balance of youth and experience, and I’m really looking forward to working with bowling coach Alan Richardson.
“I would also like to thank Cricket West Indies for allowing me the opportunity to go and experience county cricket.”