Sir William said if any unknown harmful effects emerged, they were likely to be seen in children because their bodies were still developing.
Sir William Stewart, the scientist behind the long-awaited study into mobile phone safety, told the BBC he would stop his own grandchildren using them.
It also calls on mobile phone companies not to aim their advertising at children, and for a review into the planning procedures governing the siting of transmitter masts.
Although he said he would continue using his mobile, Sir William told BBC Radio 4's Today programme: "I have got a grandchild of four and a grandchild of two and I would not be recommending that they have mobile phones."
Sir William said if any unknown harmful effects emerged, they were likely to be seen in children because their bodies were still developing.
The 10-month Stewart inquiry report, published on Thursday, recommends a "precautionary approach".
The use of mobile phones is not totally "without potential adverse health effects", it says.
Sir William said: "The balance of evidence suggests that mobile phone technologies do not cause adverse health effects on the general population of the UK.
"But there's some preliminary evidence, and I emphasise very much preliminary evidence, that emissions from mobile phones may cause in some cases subtle biological changes."
He said this did not mean the effects led to disease, but stressed it was a "new technology" and recommended precautions until more information became available.
It is thought children could face more potential health risks from mobile phone emissions because their skulls are thinner and their brains are still developing.
The far-reaching inquiry took evidence from experts across the country and its panel included experts in physics, telecommunications, engineering, and neuroscience.
It was commissioned in response to fears that mobile use could be linked to memory loss, and even Alzheimer's disease.
Among the actions the reports recommends are:
Approximately 24m people in the UK use mobile phones - a quarter of these are children.
Public health minister Yvette Cooper told the BBC: "We need to introduce a widespread programme of research into these issues, but in the meantime we will be circulating the recommendations of the Stewart report to parents across the country.
"As a parent I think it must be sensible to have a more cautious approach when it comes to children's health."
Ms Cooper said ministers would talk to the mobile phone industry over Sir William's recommendations that mobile phones should not be promoted to children.
A consultation exercise on changes to the planning process for transmitter masts would also be launched.
A spokesman for the Federation of the Electronics Industry (FEI) welcomed the report.
He said: "We are pleased this independent report builds on the general approach taken so far by the industry.
"We particularly welcome Sir William Stewart's confirmation that 'the balance of evidence does not suggest mobile phone technologies put the health of the general population of the UK at risk.
"The industry will continue to support scientific research internationally within the framework of relevant World Health Organisation recommendations. In consultation with Government, we will support the research programme proposed by the report."