The Australian succeeds Mark McCall, who resigned last month following the province's 32-14 defeat to Gloucester in the first round of Heineken Cup fixtures.
Williams will meet the squad on a short trip to Belfast later this week but will take over permanently at the end of January.
Caretaker coach Steve Williams will remain in charge for Ulster's next three games - against Munster in the Magners League and the Heineken Cup ties with Bourgoin and Gloucester.
Williams has previously coached New South Wales and Leinster, where he won the Celtic League and reached the semi-finals of the Heineken Cup.
Williams won just three of 17 Tests during a controversial 16-month stint in charge of Scotland and has most recently been coaching West Harbour in the Sydney club competition.
He was offered the Ulster post before Christmas and informed chief executive Michael Reid of his decision to accept on New Year's Eve.
Williams takes over an Ulster side level with Connacht at the bottom of the Magners League, with just two wins from nine games.
Ulster are also yet to win a game in the Heineken Cup.