The announcement was made by a spokesman for the Popular Mobilisation (al-Hashid al-Shaabi), a force comprising dozens of Shia militias.
He said the operation would see government troops and militiamen move southwards from Salahuddin province and seek to cut off IS militants in Ramadi.
The provincial capital fell to IS this month after Iraq’s army withdrew.
Since then government forces have been massing for a counter-attack in the western province, and they say they have regained some ground east of Ramadi in the past few days.
Yesterday, fighting was reported south and west of Ramadi, as the Iraqi forces tried to cut off supply routes to the city.
The offensive has been welcomed by the Americans, with Vice-President Joe Biden pledging full US support, the BBC’s defence correspondent Jonathan Marcus says.
But he adds that Washington remains uneasy about the prominent role of Shia fighters, many of whom are backed by Iran.
Separately, French Foreign Minister Laurent Fabius criticised the Iraqi government, saying Paris had joined a US-led coalition last year in carrying out air strikes against IS on the basis that Baghdad represented the interests of all groups in the country.
“There is no military solution without a political solution. In September, we linked the coalition’s support to political commitments by the new Iraqi government, what we call an inclusive policy,” Mr Fabius was quoted as saying by Reuters.
“This contract is what justified our military engagement and I say clearly here that it must be better respected,” he added.
The Popular Mobilisation’s spokesman, Ahmed al-Assadi, told a televised news conference that the operation to regain control of Anbar would be called “Labayk ya Hussein” (“At your service, O Hussein”) – a reference to a revered Shia imam.
By contrast, the Iraqi government has not been particularly effective at public relations. It has often been slow at telling people of its achievements, and foreign journalists in Baghdad sometimes have problems trying to find out what the forces are doing and how they are succeeding.
The result is that there has been real scepticism internationally about the Iraqi government’s claims to be pushing IS back on almost all fronts.