Edwards, 26, will join the county at the beginning of July after taking part in the West Indies' series against Australia, provided the move is approved by the West Indies Cricket Board.
The capture of Edwards ends several months of frustration for the county, whose director of cricket, Steve Rhodes, has been unsuccessful in bids to secure the services of Umar Gul, Ashley Noffke and Shane Bond.
"We said we would try and act quickly once the Shane Bond deal never materialised and I am delighted to be able to get someone of Fidel's quality," said Rhodes.
"This move has been bubbling along for quite a while and he is desperate to come over and make his mark in county cricket in this country.
"When he comes over the wickets should be drying out nicely and he will be a danger to all batsmen. He also has that ability to reverse swing the ball."
Rhodes added that he did not forsee any problems getting clearance for Edwards to make the move. "I understand the West Indies Board are keen for their players to come to England and taste county cricket," he said.
Edwards has taken 75 wickets in 30 Tests for the West Indies.