Right-wing ideology is losing its grip on the Conservatives and the party now realises it can only win from the centre ground, Sir John Major has said.
Sir John refused to name the candidate he will back
The ex-prime minister says the Tories could see a change in their fortunes if they tackle people's everyday concerns.
Sir John refuses to say which of the two leadership contenders he favours.
David Cameron is in Birmingham to launch his campaign to win over Tory members. Rival David Davis says he has a "mountain to climb" but can win.
The two contenders have six weeks to battle for the votes of the 300,000 Tory members who will decide the leadership contest. The result is due on 6 December.
Aides to Mr Davis say the next three weeks will prove vital as many Tory members will vote as soon as they receive their ballot papers.
Sir John said he hoped that whoever won the contest would appoint figures such as William Hague, Ken Clarke and Liam Fox to his shadow cabinet.
He included Mr Davis in the list but not Mr Cameron - which some observers will take as a hint that he expects Mr Cameron to emerge as leader.
The new Tory team could outshine Labour, Sir John told the BBC's Sunday AM programme.
Mr Cameron is launching his campaign in Birmingham
"This may be a moment when the terms of political trade begin to change," he said.
Sir John said "the infection of too much ideology has drained away" as the Conservatives became ready to fight hard to return to government.
In his membership campaign launch, Mr Cameron will try to take on Mr Davis' claim to be the "Heineken" candidate who can reach the parts of Britain other Tories have not.
Speaking at the Balsall Heath project in Birmingham, Mr Cameron will say his party must be "a party of the cities as well as the countryside and suburbs".
"Conservative revival will only take place if we show how much Conservative values are the right way to deliver a real urban revival," he will say.
"Modern compassionate Conservatism means recognising that we are all in this together and have a shared responsibility to deal with these problems."
Mr Cameron won the backing of former deputy prime minister Lord Heseltine, who said the 39-year-old had an "elusive quality that encapsulates people".
Mr Davis is in his Howden and Haltemprice constituency in Yorkshire on Sunday but will launch his campaign for members' votes in London on Tuesday.
In an interview with the Mail on Sunday, Mr Davis says people should not take too far the image of him as a "tough guy from the backstreets".
He says people warm to him when they meet him.
And in apparent dig at Mr Cameron, he adds: "The next general election is not going to be won on the basis of show business but whether people think the leader of the Conservative party can solve people's problems."
Former Tory leader William Hague says the six-week nationwide leadership campaign will do the parties a "power of good".
"At the end of that they will be more experienced, more battle hardened and will have had to be more specific about what they will do," he writes in the News of the World.