The board of trustees agreed to follow an overwhelming vote by members last month that the activity should end.
The Hunt Saboteurs Association predicted some hunts would fold as a result of the decision.
Other opponents, who have for years fought for the trust to ban “trail” hunting, were also jubilant.
They argue “trail” hunting is a smokescreen for chasing and killing real wildlife including foxes. Hunters have claimed that since chasing foxes was banned in 2004, they follow an artificial scent trail to stay within the law.
But the trust temporarily stopped issuing licences last year after the leak of webinars at which leading hunt figures discussed tactics including how to create the appearance of following scent trails.
Other landowners, including United Utilities and Forestry England, also suspended the activity on their land.
As a result of the online meetings, Mark Hankinson, director of the Masters of Foxhounds Association was found guilty and ordered to pay £3,500 – in what was seen as a landmark ruling.
Earlier this month, Natural Resources Wales announced a permanent ban on “trail” hunting.
Lee Moon, Hunt Saboteurs Association spokesperson, said: “The National Trust board have made the only conscionable decision, listened to their membership and permanently banned ‘trail hunting’ from the organisation’s 620,000 acres.
“Along with the recent Natural Resources Wales’ decision, over a million acres of countryside have been denied to hunts with more to surely follow.
“We expect to see some hunts fold completely and others face an increasingly difficult future as they struggle for land on which to carry out their illegal acts.
“We’re increasingly seeing councils deny the hunts use of their facilities on Boxing Day and New Year’s Day, further sign if any were needed, that ordinary people are sick of the hunting community and their blatant disregard for the law.”
The League Against Cruel Sports cautiously welcomed the National Trust decision, but said it was concerned it did not go far enough, because without a “full and explicit ban”, foxhunting could still take place.
Chris Luffingham, director of campaigns, said: “Their members’ voices could not have been louder, sending a clear message to the board of trustees that enough is enough and trail-hunting should be banned on trust land.
“The board has recognised the strength of feeling in its membership and the public in general, who are more aware than ever that so-called trail- hunting is used as an excuse – a smokescreen – for illegal hunting.
“However, the recent Hankinson verdict has shown that the hunting community cannot be trusted from the top down, and not having a definitive ban could lead to foxes being chased and killed by hunts.”
Leading wildlife campaigner Dominic Dyer said the decision now also put pressure on the government to ban trail-hunting.