Downing Street's defunct online petition page has been replaced with a new website that will give the public a "megaphone" to make themselves heard.
Commons Leader Sir George Young said any campaign on the site that was backed by 100,000 signatures would trigger consideration for debate in Parliament.
It will be up to the Commons backbench business committee to assess all petitions that qualify and decide whether they should be given time from the 35 days it is allocated each session for non-governmental business.
No 10's e-petition site was suspended ahead of the general election then shelved by the coalition.
It had been host to a series of highly embarrassing campaigns during the Labour years, including demands for former prime minister Gordon Brown to quit, backed by nearly 100,000 signatures.
Shortly after its launch in November 2006, it attracted 1.6 million signatures from voters opposed to plans to introduce road pricing.
The new version will operate under the DirectGov banner rather than be linked to Downing Street.
Sir George said it was a "step towards a more accessible and transparent" Parliament.
He added: "In recent weeks, Parliament has been at the centre of public interest, by leading the debate on phone hacking allegations.
"But this shouldn't mean that Parliament becomes complacent. There's much more that we can do to build confidence in the work of the House of Commons and we should continue to find new ways of encouraging people to engage. The public already have many opportunities to make their voices heard in Parliament, and this new system of e-petitions could give them a megaphone."