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.

Thomas Orchard, 32, who had schizophrenia, died in October 2012.
An Emergency Response Belt was held around his mouth when he threatened to bite, police said.
Custody sergeant Jan Kingshott, 44, and civilian detention officers Simon Tansley, 38, and Michael Marsden, 55, all deny manslaughter.
The defence said the belt was "unfortunately" what officers had been equipped with.
Mr Tansley's barrister, Michael Mather-Lees, told the court: "It looks appalling but unfortunately this was the item they had been given. It was approved, tested, trained upon and given to use as a spit or bite mask."
Prosecutors previously told the court there was no evidence Mr Orchard tried to bite Mr Tansley, who held the belt around Mr Orchard's mouth.
However, Mr Mather-Lees said the CCTV footage showing police treatment of Mr Orchard in his cell "doesn't show everything - it doesn't show every angle".
Mr Orchard, who had been arrested in Exeter on suspicion of a public order offence, was left lying face down on a mattress in his cell at Heavitree Road police station after he was freed from restraints.
Officers discovered he was not breathing when they re-entered the cell 12 minutes later, Bristol Crown Court had heard.
Mr Mather-Lees told the court Mr Tansley would have acted had he been aware that Mr Orchard was having problems breathing.
Mr Orchard, who had not been taking his medication for schizophrenia, died in hospital following a cardiac arrest.
The trial continues.

The 14-time Grand Slam title winner will therefore miss November's ATP World Tour Finals in London.
Nadal, 28, made his announcement after losing 6-2 7-6 (7-4) to Croatian teenager Borna Coric in the quarter-finals of the Swiss Indoors on Friday.
"I'm not going to Paris and London - I'm not competitive enough," the nine-time French Open champion said.
"I am going to have surgery on 3 November."
Nadal had already qualified for the ATP World Tour Finals event, so the Spaniard's withdrawal means the player ranked ninth in the final ATP Race to London rankings will make it through to the season-ending event at the O2 in Greenwich.
Britain's Andy Murray will compete in next week's Paris Masters, which is the final ranking event of the season.
The Scot, 27, currently lies in eighth position in the Race to London standings.
The Swiss Indoors in Basel was just the third tournament Nadal had played since Wimbledon following a wrist injury, and he revealed earlier this month that he was on a course of antibiotics for his appendix.
Coric, 17, showed no fear as he raced into a 5-0 lead against a wayward Nadal and held his nerve to secure a stunning victory.
Coric learned his tennis travelling between Zagreb and north London under the guidance of British coach Ryan Jones, although the pair have gone their separate ways in recent days.
The Croat goes on to face Belgian David Goffin in the semi-finals, with Ivo Karlovic up against Roger Federer, who beat Grigor Dimitrov 7-6 (7-4) 6-2.
West Indies have appointed former Australia batsman Stuart Law as their new coach on a two-year contract.
[NEXT_CONCEPT]
An "appalling" looking belt used to restrain a man who died after having a cardiac arrest in a police cell was "not ideal", a court has heard.
[NEXT_CONCEPT]
Rafael Nadal has confirmed he will not play again this season and says he will undergo appendix surgery next month.