David Cameron will insist that the drive for a change in the UK's relationship with Brussels is not "Mission Impossible" as his reform agenda enters its next phase.
The Prime Minister is writing to European Council president Donald Tusk setting out his objectives for Britain's renegotiation ahead of the in/out referendum he has promised by the end of 2017.
He will call for reforms to welfare rules in a bid to curb the number of European citizens coming to Britain, including barring EU migrants from claiming tax credits and child benefit until they have lived in the UK for at least four years.
Mr Cameron will also demand "legally binding and irreversible" changes to exempt the UK from "ever closer union" with the rest of the European Union, measures to protect the single market for Britain and other countries outside the eurozone and reforms to cut the burden of red tape on business.
In a speech in London to coincide with his letter to Mr Tusk, the Prime Minister will acknowledge he faces a "big task" to get the changes he wants but the problem is "eminently resolvable" if European leaders demonstrate the political will and imagination to work with him.
Setting out his four objectives, he will say that he wants measures to protect the single market for the UK and other countries that do not use the euro.
That would mean a "set of binding principles that guarantee fairness between euro and non-euro countries," he will say.
The second goal is to "write competitiveness into the DNA of the whole European Union", including by "cutting the total burden on business".
The third aim is to exempt Britain from an "ever closer union", while bolstering the role of national parliaments across the EU.
Mr Cameron will stress this must be done "not through warm words but through legally binding and irreversible changes".
The fourth aim - potentially the most difficult to achieve - will be to "tackle abuses of the right to free movement, and enable us to control migration from the European Union, in line with my manifesto".
The Conservative general election manifesto said: "We will insist that EU migrants who want to claim tax credits and child benefit must live here and contribute to our country for a minimum of four years."
There had been speculation that Mr Cameron is ready to drop the demand, as other EU leaders regard it as breaching the principle of free movement of labour.
Mr Cameron is expected to set out new analysis of the amount of benefits being claimed by EU migrants as he makes his case for reform.
Government sources said that around 40% of EU migrants were supported by the UK's welfare system during their first four years in the country - some 244,000 people out of 526,000 new arrivals.
Some 66% of those, around 148,000, were receiving in-work benefits such as tax credits, the analysis of Department for Work and Pensions figures revealed.
More than 10,000 newly arrived EU families were claiming more than £10,000 a year through in-work welfare in 2013, according to the analysis.
In his speech the Prime Minister will insist that it is possible for his goals to be met, which will then allow him to recommend a vote to remain in the EU when he calls his referendum.
"There will be those who say - here and elsewhere in the EU - that we are embarked on Mission Impossible," the Prime Minister will say.
"I say: why? I do not deny that seeking changes which require the agreement of 27 other democracies, all with their own concerns, is a big task.
"But an impossible one? I do not believe so for a minute."
The Prime Minister will insist he has a track record of achieving change in Brussels, including cutting the EU's budget, exempting Britain from the bail-out scheme and using the UK's veto to protect the country's national interest.
He will say: "When you look at the challenges facing European leaders today, the changes that Britain is seeking do not fall in the box marked 'impossible'.
"They are eminently resolvable, with the requisite political will and political imagination.
"The European Union has a record of solving intractable problems. It can solve this one.
"Let us therefore resolve to do so."
Putting the UK's demands into writing will mark the start of the "next phase" of the renegotiation agenda, Downing Street said.
As part of a fresh diplomatic push alongside the publication of the reform plans, Chancellor George Osborne will meet European Commission president Jean-Claude Juncker in Brussels, while the Prime Minister will have the chance to discuss the issues with European counterparts at an international summit in Valletta, Malta tomorrow.
Europe minister David Lidington will answer MPs' questions on the Prime Minister's reform agenda when he makes a statement in the House of Commons.