Organisations given UK government grants will be banned from using the money to try to persuade ministers to change the law or increase spending.
A new clause will be added into all new and renewed grant agreements to ensure funds are spent on good causes, rather than on political campaigns.
Cabinet Office minister Matthew Hancock said "the farce of government lobbying government" had to stop.
Voluntary groups said the rules could threaten their freedom to speak out.
Critics also said the restrictions, which come into effect in May and will only apply to grants from central UK government departments, could be hard to enforce.
According to a House of Commons briefing, the estimated total income of the UK voluntary sector (not including charities) in 2012-13 was £40bn, of which £13bn came from government grants.
The Cabinet Office said UK government departments gave the voluntary sector just under £10bn in grants last year.
Under the new conditions, organisations will not be able to use grants for "activity intended to influence - or attempt to influence - Parliament, government or political parties".
Charities will still be able to use privately-raised funds to campaign as they like.
'Uncomfortable for government'
Mr Hancock said: "The public sector never lobbies for lower taxes and less state spending, and it's a zero sum game if Peter is robbed to pay Paul."
But a senior charity source told the BBC it was an attack on freedom of speech.
"Charities are not only about Tiny Tim on his crutch, but espousing the cause of the disadvantaged," the source said.
"That will sometimes be uncomfortable for any government."
BBC political reporter Alan Soady said exactly how such a rule would be enforced - and how charities would prove which pots of money funding for lobbying came from - was still unanswered.
There was also some concern in Whitehall that some charities seemed to have been set up primarily to lobby, or that they were straying from their brief on the issues they lobbied on, he said.
The move follows work by the right-of-centre think-tank the Institute of Economic Affairs (IEA) into so-called "sock puppets", where taxpayers' money is given to pressure groups which then campaign for policy changes or extra money.
Chris Snowden, the organisation's head of lifestyle economics, said: "At every level - local, national and European - people have been subsidising political campaigns that they may not know about and might disagree with.
"Campaigning is an important part of a thriving democracy but charities and pressure groups should not be doing it with taxpayers' money."
Former Bishop of Oxford Lord Harries, who chairs a commission which has looked into charity lobbying - the Commission on Civil Society and Democratic Engagement - said the "polarisation" between charities' direct work and policies they wanted to change was "very, very unhelpful".
Charities on the "front line" could often best identify where government policy was failing, and "surely they are morally bound to tell the government they could improve their work to help, say, children in poverty?" he said.
Trying to separate where lobbying money came from would be a "bureaucratic nonsense", he added.
Sir Stuart Etherington, chief executive of the National Council for Voluntary Organisations - an umbrella body for the voluntary sector in England - added his concern, warning that the "draconian" new rules could force charities to take a "vow of silence".
"The new rules attached to grant income would appear to prevent charities from suggesting improvements or efficiencies to civil servants or ministers, or even from raising concerns with MPs, for example about the treatment of vulnerable people."
The system has been trialled in grants provided by the Department for Communities and Local Government.
Ministers insisted it had not curtailed the ability of charities such as Shelter from lobbying on housing legislation.