The Justice Secretary also claimed that businesses can benefit from giving training and work to convicts, while also helping to pay for the running costs of their jails.
Timpson, the locksmiths and shoe repairers, has become the first major British company to open workshops for serving prisoners but Virgin and Marks & Spencer are also "expressing a strong interest".
The BBC held discussions about using inmates to work on its historic programme archives but no deal was ever signed.
Ministers stress the initiative is intended to help cut re-offending rates rather than rewarding criminals or using them as a source of cheap labour.
Currently 47 per cent of adult offenders who are jailed re-offend within 12 months of release, while the prison population in England and Wales has risen sharply in recent years to reach a record 88,000 in recent months.
Mr Clarke said: "Introducing work experience and training to people who are serving their time and being punished in prison is altogether a more intelligent way of running the prison service.
"There is no doubt that people who get sent to prison have made a mistake, society is entitled to look for them to be punished, but also society should be trying to do something to help those who have the gumption to sort themselves out, to resume an ordinary honest life as decent citizens when they leave.
"If you just incarcerate people, if prison is just a warehouse in which you keep people and then release them without guidance into the world, it's hardly surprising that half of them will be back within 12 months, having committed more crime.
"Many prisoners do not want to be part of that cycle. We need to facilitate the way in which people get back into a normal life and do not commit further crimes again."
He added: "We also stress to the businessmen that you can take part in this and derive benefits as a business and you don't have to compromise your ordinary standards of commercial judgment.
"I want eventually to see businesses manufacturing, providing services, from prisons on a commercial basis.
"There's no reason why they shouldn't help pay for themselves and the cost of the prison."
He is telling big name employers: "You will be able to recruit and train people who will be highly motivated individuals when they've taken advantage of the opportunities this kind of thing can present them."
The Prison Industries unit is being replaced by an organisation called One3One Solutions that will help offenders improve their job prospects.
But "normal household name firms" are being encouraged to carry out more of the work "as part of their social responsibility", according to Mr Clarke.
Timpson opened its first training academy in Liverpool four years ago and now has another in Kent where prisoners serve members of the public as well as learning key-cutting and shoe-repairing.
On a visit this week, Mr Clarke described it as a "positive, sensible" way of combining punishment and rehabilitation compared with some prisons that are "just teeming dreadful places in which bored people sit around until they are released and commit further crime".
According to Timpson management, just seven of more than 200 prisoners it has employed have ended up behind bars.
