The leader said he would pay for the abolition through a crackdown on loopholes for the better-off and by dealing with tax evasion better.
The announcement was made as the party prepares for its annual conference in Brighton, which begins this weekend, and just days after the SNP announced it was making £20 million available to those suffering because of the tax.
The cash prompted a row as opposition parties and charities warned £50 million was needed to cancel out its effects.
Mr Miliband is expected to say the bedroom tax has become a symbol of an out-of-touch Government which stands up only for the interests of the wealthy.
He will say: "We have a Tory-led Government which listens only to a privileged few.
"I am leading a different Labour Party, a One Nation Labour Party, which listens to, and will stand up for, ordinary families like that of Danielle Heard, who I met this week.
"We'll fight for her like she has fought cancer heroically for 14 years. She is disabled and battling cancer again. But now her family must pay £80 a month they can't afford under this government's hated bedroom tax."He will add: "We will scrap that tax. And what's more I can tell you how.
"We'll scrap the bedroom tax by abolishing the shady schemes of tax loopholes for the privileged few, which the Tories keep inventing. Tax cuts for hedge funds, the billion pound black hole created with a scheme for workers to sell their rights for shares, and by tackling scams which cheat the taxpayer.
"That's what a One Nation Labour government will do. That's a party that will fight for you."
The party estimates that scrapping the hedge fund measure will raise £150m.
It warns the "shares for rights" scheme has opened up a tax loophole of up to £1bn, and says tackling tax scams in the construction industry could realise £500m.
The Treasury has estimated the bedroom tax, officially the "spare room subsidy" will raise £470m.
The TUC welcomed the announcement, saying the 'bedroom tax' was a "cruel policy that is hitting vulnerable people in desperate need of help".
Scottish Labour Leader Johann Lamont said: "It's now clear that the quickest way to abolish the bedroom tax is to elect a Labour government in 2015. TUC General Secretary Frances O'Grady said: "Scrapping it will ease the fears of thousands of low-income families and disabled people."