The peer, who was Margaret Thatcher’s most successful chancellor, said the EU has become a "bureaucratic monstrosity" and
that the benefits of leaving "would substantially outweigh the costs".
Lord Lawson said it was pointless to try to improve terms on Britain’s EU membership ahead of a an in/out referendum in 2017 and that Mr Cameron has to resign himself to four years of "inconsequential” negotiation with his EU partners.
Lord Lawson – who voted for Britain to join the EU in 1975 – said he would be backing Britain’s exit in 2017.
His comments are likely to add pressure to the Prime Minister to offer concessions to the Tory right after the strong advances made by the United Kingdom Independence Party in the local elections last week.
Writing in The Times, he said that "the case for exit is clear”, insisting that monetary union "has fundamentally changed the nature of the European Union and of non-Eurozone Britain’s relationship with it.
"Not only do our interests increasingly differ from those of the eurozone members but, while never ‘at the heart of Europe’, we are now becoming increasingly marginalised as we are doomed to being consistently outvoted by the eurozone bloc.”
Lord Lawson knocked back any suggestions that there would be "a heavy economic cost, making this unwise” because "the economic gains would substantially outweigh the costs.
"The only gain that can be clearly quantified is that we would no longer pay our annual membership fee of some £8 billion.
"That is the size of our annual net contribution to the EU budget, even after the benefit of the Thatcher rebate.”
There were other gains too, he said, notably that Britain would no longer be subject to EU regulation and red tape which "imposes substantial economic costs on all member states”.
Removing Britain from the EU would also result in saving the City from an EU "frenzy of regulatory activism, of which the foolish and damaging financial transactions tax, imposed against strong UK opposition”.
He added: "Those who claim that to leave the EU would damage the City are the very same as those who in the past confidently predicted, with a classic failure of understanding, that the City would be gravely damaged if the UK failed to adopt the euro as its currency.”
The peer, who was Chancellor from 1983 to 1989, said that it was likely that a Labour leader would have to promise a vote on Britain's membership of the EU ahead of the election, making a referendum almost certain to take place.
The Prime Minister was pointlessly trying to "renegotiate improved terms for the UK within the Union, which he can then put to the people in a referendum in 2017”, he said.
He added: "We have been here before. He is following faithfully in the footsteps of Harold Wilson almost 40 years ago.
"The changes that Wilson was able to negotiate were so trivial that I doubt if anyone today can remember what they were. But he was able to secure a 2-1 majority for the "in” vote in the 1975 referendum.
"I have no doubt that any changes that Mr Cameron — or, for that matter, Ed Miliband — is able to secure will be equally inconsequential.”