The announcement was made by a spokesman for the Popular Mobilisation (al-Hashd al-Shaabi), a volunteer force comprising dozens of Shia militias.
The operation would see troops and militiamen move southwards from Salahuddin province and seek to cut off IS militants in Ramadi, he said.
The provincial capital fell to IS this month after Iraq’s army withdrew.
Since then government forces have been massing for a counter-attack, and they say they have regained some ground east of Ramadi in the past few days.
On Tuesday, 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.
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.
He said the operation would “not last for a long time” and that new weapons would be used in the battle that would “surprise the enemy”.
Mr Assadi separately told the AFP news agency that a mix of security forces and paramilitaries would move into desert areas north-east of Ramadi, before encircling the city and preparing to retake it.
Islamic State is extremely good at public relations. It generates admiration and fear with each of the videos it issues – 360 within the last year, just about one a day.
The terror it generates through its gruesome execution videos does a great deal of its work for it. And people around the world believe that it is indeed carrying all before it.
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.
When the Prime Minister, Haider al-Abadi, told the BBC that his forces would recapture Ramadi within days, there was widespread disbelief; even though Western diplomats in Baghdad have been forecasting very much the same thing.
In an interview with the BBC on Monday, Iraqi Prime Minister Haider al-Abadi said Ramadi might be recaptured “within days”.
Mr Abadi also defended the decision of the 1,500 soldiers who had reportedly been stationed in the city to flee in the face of an assault by as few as 150 militants.
He explained that the soldiers had been fazed by Islamic State’s shock tactics and did not lack the will to fight, as alleged by US Defence Secretary Ashton Carter.
“I am sure he [Mr Carter] was fed with the wrong information”.
“They have the will to fight but when they are faced with an onslaught by [IS] from nowhere… with armoured trucks packed with explosives, the effect of them [being blown up] is like a small nuclear bomb – it gives a very, very bad effect on our forces,” he added.
IS seized parts of Ramadi, which is only 100km (60 miles) west of the capital Baghdad, along with the nearby city of Falluja and much of Anbar in January 2014.
The province – which is predominantly Sunni – covers a vast stretch of the country west from Baghdad to the Syrian border, and contains key roads that link Iraq to both Syria and Jordan.
The US had urged the government not to send Shia militias in Anbar in case they drove more of Anbar’s Sunnis into supporting the jihadists.
But after IS took complete control of the provincial capital, the Popular Mobilisation was deployed. On Saturday, it retook the town of Husayba, east of Ramadi.
Mr Abadi also told the BBC that the US-led coalition needed to help Iraq tighten control of its borders, as many IS fighters were slipping into the country from Syria.