The Pakistan Cricket Board (PCB) announced that the 42-year-old Misbah will continue to lead Pakistan in the three-match Test series scheduled from April 22.
The Tests will be preceded by a limited-overs series of four Twenty20s and three one-dayers.
The PCB said in a statement that Misbah has conveyed his availability for the tour to Board Chairman Shaharyar Khan.
"Accordingly the Chairman has approved his appointment as captain of the Pakistan test team for the upcoming Test series in West Indies," the statement said.
Sarfaraz is already the captain of the ODI and T20 national sides after Azhar Ali stepped down as captain of the one-day team at the start of the Pakistan Super League last month.
The announcement brings to an end a debate which has been raging since last month on whether Misbah would continue as captain or batsman for the tour of West Indies.
Misbah had earlier said he wanted to carry on playing as batsman and do well for his team but it was up to the board to appoint him as captain or not.
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