Logie, interim coach during the recent home series against Australia and Sri Lanka, has agreed a two-year contract.
West Indies lost against Australia 3-1 but made Test history in the last match, recording the highest ever fourth innings winning total. They beat Sri Lanka 1-0.
Logie, 42, said: "We started something with this team ... against the Australians which has worked for us and we will be looking to continue in this vein."
Logie played 52 Tests for West Indies between 1983 and 1991, scoring 2,470 runs at an average of 35.79. He replaces Roger Harper, the former off-spinner and all rounder, who is now an academy coach in Grenada.
