The 48-year-old will work under new director of cricket Jimmy Adams and chairman of selectors Courtney Browne, both former Windies internationals.
Law had previously coached Sri Lanka and Bangladesh's national sides.
"I am excited at the opportunity to contribute to what I think is an interesting time for West Indies," said Law, who takes over on 15 February.
"I think this assignment has come at an important time of my career."
West Indies had been without a full-time head coach since Phil Simmons was sacked in September.
Having also had time in charge of Bangladesh Premier League side Khulna Titans, Law becomes the third Australian to coach the Windies after Bennett King (2004-07) and John Dyson (2007-09).
While he only played one Test in 1995 - scoring 54 not out in his only innings - Law appeared in 54 one-day internationals between 1994 and 1999, and was a losing finalist in the 1996 World Cup.
As well as captaining Queensland to their first Sheffield Shield win in 1994-95, he was one of the leading batsmen in English county cricket in long stints with Essex and Lancashire, as well as having a brief spell at Derbyshire at the end of his career.
West Indies have appointed former Australia batsman Stuart Law as their new coach on a two-year contract.