In a Commons statement, Mr Meacher said the Government would bring forward legislation on the issue as soon as Parliamentary time allowed, and he expected that before the next general election.
To the cheers of Labour MPs, he said he was committed to meeting his party's manifesto pledge on a freedom to roam for walkers and ramblers across mountain, moor and heathland in England and Wales.
But the opposition accused the Government of "class warfare" and warned that the measures would be overly bureaucratic and could ruin the environment.
Mr Meacher said the statutory right would be balanced by "proper and reasonable limitations" and would not apply to developed or agricultural land.
A law was needed because the voluntary approach to opening up the countryside had delivered "relatively little" over the last 50 years.
"Glorious parts of our heritage are still the preserve of the few, not the delight of the many," he told MPs.
"Only a new statutory right will deliver cost-effectively the extent and permanence of access we are seeking.
"We are now convinced that legislation is the only way to make sure people will be free in perpetuity to explore open countryside."
Mr Meacher said there was no question of giving people a "right to trample over crops or through other people's gardens", and Local Area Forums would address concerns and issues over "fragile" countryside areas.
Gillian Shephard, the shadow environment secretary, said voluntary agreements between landowners and ramblers were a much better way of gaining increased access. Mrs Shephard, amid barracking by Labour MPs, said: "We deplore that you have sought to alienate the very people who have done so much to promote access in all parts of the country.
"It is regrettable, although perhaps only to be expected from someone who has talked about land-owning as `exclusivity' and `inherited privilege', that you should squander the goodwill which those in the countryside have sought to bring to this issue."
Mrs Shephard demanded compensation for landowners and farmers for costs of access and loss of land value.
She added: "You have produced a solution which has the potential of satisfying no one. It will be cumbersome, it will be bureaucratic and it will further divide town and country. It is a squandered opportunity."
Matthew Taylor, for the Liberal Democrats, said the minister's statement was "a big step from notional rights to legal realities".Reuse content