But some child protection campaigners fear it will be easier for adults in positions of trust to abuse children.
The change is part of the government's Freedoms Bill, published earlier.
National security Mr Clegg said: "Of course we need checks on those people who are working regularly with children and vulnerable adults but not everybody who is volunteering, often on an irregular basis, simply trying to help out. We want to get it into proportion.
"Most people accept we were treated with too much distrust and suspicion and too many people were almost treated as if they were criminals by Labour in recent years. End Quote Tim Loughton Children's minister
"It's still going to be a scheme of some considerable size but one which does not cast that atmosphere of distrust over adults who are simply trying to do their best by their own children, by children in their own community."The bill also includes limits on police stop and search powers, ends indefinite storage of innocent people's DNA and gives residents more control over CCTV.
The vast majority of the one million people on the DNA database who have been arrested but not convicted of a crime will be removed from it within months of the bill becoming law.
But police will retain the right to keep DNA of people deemed to be a risk to national security, even if they have not been convicted of an offence.
Where someone has been charged with a serious crime but not convicted, their DNA profile will be held for three years with a possible two-year extension with court approval.
Stop and search powers will be much more specifically targeted in future if the bill becomes law.
'Streamlined' The new bill calls for a merging of the Criminal Records Bureau (CRB) and Independent Safeguarding Authority to form "a streamlined new body providing a proportionate barring and criminal records checking service".
That body will provide what ministers say will be a more "proportionate" checking service for about 4.5 million people who work "closely and regularly" with children or vulnerable adults.
Teachers will continue to be vetted - but those who do occasional, supervised volunteer work will not.
Job applicants will also be able to see the results of their criminal record check before their prospective employer so mistakes can be corrected.
And the bill promises a "portability of criminal records checks between jobs to cut down on needless bureaucracy" and to stop "employers who knowingly request criminal records checks on individuals who are not entitled to them".
'Completely wrong' Home Secretary Theresa May suspended Labour's Vetting and Barring scheme in June 2010 and ordered a review be carried out.
The scheme was set up in 2009 after an inquiry into the murders of the Soham schoolgirls Holly Wells and Jessica Chapman by school caretaker Ian Huntley.
Children's minister Tim Loughton said: "The new system will be less bureaucratic and less intimidating. It will empower organisations to ask the right questions and make all the appropriate pre-employment checks, and encourage everyone to be vigilant.
End Quote Mark Williams Thomas Child protection expertThis is simply about saving money”
"Protecting children and keeping them safe remains our top priority, but it's also important that well meaning adults are not put off working or volunteering with children."Children's charity Barnardo's said the move was "a victory for common sense".
Chief executive Anne Marie Carrie said: "There is already enough safeguarding in place for people who have unsupervised, substantial access to children.
"This approach will make it easier for grandparents, parents and neighbours who should be able to play an important role in a child's life without unnecessary red tape."
However, former police detective and child protection expert Mark Williams Thomas has told the BBC he believes the changes will give offenders more opportunities to gain access to children.
"If it was about keeping children safe then this vetting scheme would continue. CRB would continue in the fashion it is," he said.
"This is simply about saving money, it's about scrapping any ideas that Labour had previously. Whoever is advising the government on this position has got it completely wrong.
"Offenders are very deviant, they're very calculated and they will seek out opportunities and they will go to where those checks don't exist."