The 33-year-old Chase replaces 32-year-old Kraigg Brathwaite, who resigned from the job in March after three years.
Chase will lead the Windies in three home Tests against Australia in June and July. The first Test in Bridgetown on Chase's home island of Barbados will also be his 50th since his Test debut in 2016.
The 1.96-metre off-spinner has taken 85 wickets at 46, and as a middle-order bat has scored more than 2,200 runs at 26, including five hundreds.
His best bowling figures was 8-60 against England in the second innings of a 381-run win in 2019 at his Bridgetown home ground.
Chase was shortlisted for the captaincy with John Campbell, Tevin Imlach, Joshua Da Silva, Justin Greaves and Jomel Warrican. Shai Hope, the one-day and Twenty20 captain, declined to be considered.
West Indies officials said they conducted detailed assessments of tactical approach, leadership style, communication skills and behaviour before choosing Chase.
"Our new captain has earned the respect of his peers, understands the responsibility that comes with the role, and has shown the leadership qualities we need to take this team forward," coach Daren Sammy said in a statement.
"I urge fans across the region to rally behind him - we're building something special."
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