Michael Howard will be "cheering on" David Cameron's plans to radically change the party's policies, the former Tory leader has said.
Mr Howard says the Tories are "a credible and convincing alternative"
Mr Howard, speaking on BBC Radio 4, said his successor had made a "dramatic impact" since he became leader.
He said the general election had showed the party needed a shake-up and Mr Cameron was going about it "in entirely the right way".
Mr Cameron declared 2006 would be a year of transformation for the Tories.
Mr Howard said the party had been through "difficult times" but that the new Tory leader was making great progress.
"I have a very high opinion of him. He has tremendous qualities and he has used them to the full since he gained the leadership.
"What he is about is making the Conservatives a clearly credible and convincing alternative," he said.
Former home secretary Mr Howard, who stepped down because he believed that at 63 he was too old to lead the party, said he would be supporting his 39-year-old successor from the back benches.
"I think it's the job of members of parliament, once a leader has been elected, to back his judgements. We're not a debating society."