George Osborne has opened the way for a fresh round of £10bn welfare cuts by securing agreement from the work and pensions secretary, Iain Duncan Smith, and promising the Liberal Democrats that the cuts will be balanced by a bigger contribution from the rich.

Duncan Smith had been the main Conservative obstacle to more welfare cuts but on Sunday he wrote a joint article with the chancellor saying he was "satisfied" such savings were possible.

In return, the Treasury has given him the final political go-ahead for universal credit, his cherished but risky master plan to merge benefits and tax credits from next year.

Senior Tory sources also suggested that senior Lib Dems had also accepted the fresh cuts as long as Osborne and Cameron stuck to their promises made that the rich would have to make the largest contribution to the next attack on the deficit.

Osborne and the Lib Dems have been scouring Whitehall for £16bn of further cuts to be implemented in 2015-16 ever since Osborne was forced in last year's autumn statement to concede that he could not eradicate the structural deficit in this parliament.

Although Osborne does not need to spell out the precise details of the 2015-16 deficit reduction programme until next year's autumn statement, the welfare reforms will require legislation to be in place within two years at the most. The first targets are likely to be housing benefit for the under 25s and restraint on the uprating of benefits.

Osborne's two deals – with Duncan Smith and senior Lib Dems – free the chancellor to put political pressure on Labour to explain its plans to cut the deficit.

In a joint article in the Daily Mail, Duncan Smith and Osborne state: "We are united in our determination to deliver universal credit, the most fundamental reform of our benefits system for a generation, on time and on budget."

They say that further savings are needed in most government departments and most areas of spending at the next spending review.

They also point out that the Treasury illustrated at the time of the last budget that if the rate of reductions in departmental budgets in the next spending review period is to be kept at the current rate, the welfare budget will have to be reduced by more than £10bn by 2016-17.

They write: "We are both satisfied that this is possible and we will work together to find savings of this scale."

Duncan Smith has also given ground by accepting David Cameron's commitment not to withdraw rich pensioners' access to TV licence, travel passes or winter fuel payments.

The agreement between the two cabinet members has been struck as the paper serialises a biography of Osborne that lays out some of the past heated disputes over welfare cuts between the two men.Setting out his plans for further cuts, Cameron told the BBC's Andrew Marr Show: "We are going to take further action to make sure that the richest people in our country pay a fair share towards deficit reduction. The richest 10 per cent in our country are not only paying more in income tax. They are paying a greater percentage of the total income tax take than they ever did under Labour."

Cameron also ruled out a mansion tax, the Liberal Democrats favoured means of squeezing the rich.

In his speech on Monday, Osborne will say anyone remotely serious about tackling UK's problems needs to start by setting out how savings, including in welfare, will be achieved, something Labour is intent on avoiding until next year at the earliest.

Tory strategists believe the public are in the mood to hear an honest assessment of how global forces are challenging the UK economy to be more competitive.

He will explain how in every single year of this parliament the rich will pay a greater share of our nation's tax revenues than in any one of the 13 years that Labour were in office.

The chancellor will also use his speech to announce a £1bn of joint industry, university and government funding for world-leading science projects in the UK.

The government will add £200m of new money to the Research Partnership Investment Fund, which supports university capital projects. The Fund was launched at the 2012 budget, with £100m of funding but has been heavily oversubscribed with a large number of high-calibre bids.

To access the money, universities must at least double the public funding through contributions from private companies or charities. So, by tripling the government support to £300m, the total investment, including the universities own contributions, is expected to be at least £1bn.