The 24-year-old, seen as the best bowler in the current side, resigned ahead of the home series against Pakistan starting with a Twenty20 international at Harare on Friday.
"He told Zimbabwe Cricket authorities that he has received a lucrative offer from Lancashire County Cricket Club in England, and has decided to take it up," Zimbabwe Cricket said in a statement.
"It offers him an opportunity to grow his game by playing alongside the likes of England international James Anderson and former South Africa batsman Ashwell Prince.
"Jarvis said that he has not turned his back on international cricket and that given his age, the three-year contract provides a unique opportunity to mature as a player who would then give back more then than he has been doing now," the statement added.
Jarvis follows in the footsteps of batsman Craig Ervine, who earlier this year turned his back on Zimbabwe to play club cricket in England after a series of pay disputes with the country's authorities.
Zimbabwe's leading cricketers formed a union last week and threatened to boycott the Pakistan series over unpaid salaries and future match fees, but called off their protest on Friday after assurances from the board.
Speedster Jarvis, whose father Malcolm also played for Zimbabwe, has played eight Test matches for Zimbabwe, taking 30 wickets at an average of just over 31. He has also featured in 24 one-day internationals and nine Twenty20 matches.
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