The justice secretary, Chris Grayling, is to announce a rapid expansion in the use of private and voluntary sector organisations to supervise short-sentence prisoners when they leave jail, on a "payment by results" basis.

Grayling says he wants "old lags", including former gang members, to meet newly released inmates at the prison gates to act as mentors and help them get their lives back together again.

The move represents an acceleration of the "rehabilitation revolution" by the new justice secretary, who has decided not to wait for the evaluation of pilot schemes put in place by his predecessor, Ken Clarke.

In a speech on Tuesday to the Centre for Social Justice thinktank, Grayling will confirm that the probation service will retain a critical role in managing and supervising high-risk and dangerous offenders. But he will add that the private and not-for-profit sectors are also to be given a role in supervising low and medium-risk offenders.

"The public sector will, of course, continue to have a significant role in working with offenders – particularly in guarding our society against harm. But it's time to make sure we use all of the expertise that is out there to help drive the improvements we need, " he is expected to say.

Grayling refers to a man he met a couple of weeks ago in a rehab centre in Stoke-on-Trent. "He was in his thirties, and had passed again and again through the criminal justice system. He said to me: 'When I came out of prison I wanted to get my life back together, but I just didn't know how'.

"That's a tragedy. Nearly half of prisoners themselves say they will need help to find a job when they leave prison. Over a third say they will need help to find somewhere to live when they are let out.

"When all we do is just take those people, release them on to the streets with £46 in their pockets and no other support, why are we surprised that they reoffend again quickly? Whether you are the hardest of hardliners on crime, or the most liberal observer, every single one of us has a vested interest in an enlightened approach to reducing offending, " Grayling says. "We can't just keep recycling people round and round the system."

When someone leaves prison on a sentence of less than 12 months, Grayling wants them to have a mentor and a place to live, and rehab or training lined up, and "above all" someone who knows where they are, what they are doing, and can be a friend to prevent them from reoffending. He suggests that often former offenders who have gone straight will be best for the job, saying there are really good organisations "making good use of old lags in stopping the new ones".

The announcement on Tuesday will be restricted to the release arrangements of those serving short sentences who are currently under no obligation to stay in touch after their release. The probation service only has statutory post-release supervision for offenders who have served more than 12 months. The Probation Chiefs Association has told ministers that this is "a major gap in post-sentence supervision" and should be a matter of priority.

They said short-sentence prisoners have the highest reoffending rates and so payment-by-results schemes could make the biggest impact. But they have also warned ministers not to restrict the role of the probation service to public protection and advising the courts.

Harry Fletcher, of the National Association of Probation Officers, said an announcement on the wider privatisation of the probation service had been delayed until December or even the new year.

Grayling announced last week that five prisons were to be handed over to the private sector, but the public prison service would retain "core custodial services" across the remaining 120 jails while putting ancillary services out to competition.