But he said there is "detail to be worked on" before a crunch summit on 18-19 February.
The deal, published by European Council President Donald Tusk, allows for an "emergency brake" on migrant benefits.
The BBC's Norman Smith said the document was hugely controversial and would be resisted by the PM's critics.
Everything you need to know about the UK's EU referendum
If the UK can get an agreement at the February summit, Mr Cameron is expected to hold a referendum in June on whether Britain should remain in the EU.
The European Commission said EU leaders will discuss the draft deal for the first time on Friday with the aim of getting an agreement at the February summit.
Sources in Brussels have told the BBC's Europe editor Katya Adler they are expecting criticism of Mr Tusk's proposals - but the EC President would not be publishing them if he was not confident the big European players were not on board.
"There'll be a lot of haggling, bargaining and bickering in the next couple of weeks before the summit," she added.
Europe minister David Lidington, has, meanwhile, been summoned to the Commons at 12:30 GMT to answer an urgent question on Mr Tusk's text from Labour leader Jeremy Corbyn.
'Emergency brake'
A major sticking point remains Mr Cameron's proposed restrictions on in-work benefits for EU migrants, which are seen as discriminatory by Poland and other central European nations.
The EU has rejected Mr Cameron's original call for a four year ban on migrants claiming tax credits and other in-work benefits, which he said would help bring down immigration into the UK.
Instead, officials have proposed an "emergency brake" on benefit payments, that would be available to all member states if they could prove their public services were under excessive strain.
This could be triggered within months of Britain voting to remain in the EU but would need the approval of other EU states before being applied.
London Mayor Boris Johnson, who has yet to say whether he will join the campaign to quit the EU, told LBC radio: "What would be better is if we had a brake of our own that we were able to use."
He added that there is "much, much more that needs to be done" to reform the UK's relationship with the EU.
Mr Cameron will set further details of his renegotiation demands in a speech later, including a so-called "red card" system to make it easier for member states to band together to block unwanted EU laws.
'Yellow card'
Under the current "yellow card" system, introduced in 2009, parliaments can get together to formally accuse the European Commission, the unelected body which produces EU laws and regulations, of overstepping its remit. The commission can decide to maintain, amend or withdraw the proposal.
However, it has been little used so far, with only a small number of EU laws attracting attention from a substantial number of parliaments.
The treaty rules only oblige the commission to provide a written response to complaints, justifying why a set of proposals meet the bloc's rules on "subsidiarity".
Downing Street sources said the new proposal - which would allow 55% of EU parliaments to club together to block measures - would strengthen this power and ensure the commission "cannot just ignore the will of national parliamentarians".
Vote Leave chief executive Matthew Elliott dismissed the "red card" proposal, saying: "These gimmicks have been ignored by the EU before and will be ignored again as they will not be in the EU treaty."
UKIP Leader Nigel Farage said: "The idea we are being sold that a joint 'red card' is some sort of victory is frankly ludicrous."
Britain Stronger in Europe said that the "red card" proposal and the plans to curb benefits "or equivalent concessions" would "represent a significant victory for the prime minister and underline that Britain is stronger in Europe".
Integration/Sovereignty: Allowing Britain to opt out from the EU's founding ambition to forge an "ever closer union" of the peoples of Europe so it will not be drawn into further political integration. Giving greater powers to national parliaments to block or scrap EU legislation.
Competitiveness: To extend the single market and cut down on excessive regulation - commonly known by critics as "Brussels bureaucracy".
Benefits: Restricting access to in-work and out-of-work benefits to EU migrants. Specifically, ministers want to stop those coming to the UK from claiming certain benefits and housing until they have been resident for four years. But the European Commission, which runs the EU, has said such a move would be "highly problematic" and the focus has now turned to the UK having an "emergency brake" which could stop in-work benefits to EU migrants for four years.
Eurozone v the rest: Securing an explicit recognition that the euro is not the only currency of the European Union, to ensure countries outside the eurozone are not disadvantaged. The UK also wants safeguards that it will not have to contribute to eurozone bailouts.bbc
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