The West Indies Cricket Board (WICB) said it had been informed by Skerritt of his decision to quit after the 10-wicket loss to England in the first Test, when the WICB made a public apology for the performance of the home side.
Skerritt was enraged by reports that his players partied after that defeat and had vowed to investigate the matter fully.
"Events following the first Test match in Jamaica have led me to review my role as team manager," Skerritt said in a letter to WICB president Teddy Griffith.
"I regret that, despite my best efforts, I have been unable to instil in the entire team the fullest understanding of their obligations on and off the field to the people of the West Indies."
Skerritt, who took over as team manager on March 1, 2000, said he remained committed to West Indies cricket and was keen to support his successor to ensure a smooth transition. His resignation will take effect from the end of June.
The West Indies team had apologised for its "shocking performance" in the first Test defeat in Kingston.
"The team further apologises for the inappropriate conduct of four members of the team who were seen in a party stand at Sabina Park following the loss," a WICB statement said.
Skerritt said at the time: "I am disgusted at the thoughtlessness and shamelessness displayed by these players following such an horrific performance."
