As a result, how - and not just whether - a claimant is able to accomplish tasks like walking and planning journeys will help determine the amount they are entitled to in benefits.
Claimants who manage the tasks, but not "reliably", will get higher payments.
Ministers admitted there were concerns that the proposals were "unclear".
The Personal Independence Payment (PIP) will replace the existing Disability Living Allowance (DLA) in April. People who are less mobile will be entitled to higher payments.
Campaigners had warned that people deemed capable of walking more than 20 metres could receive lower payments - even if they were unable to do so "safely, reliably, repeatedly and in a reasonable time period".
Ministers had previously denied the claim and argued that these words did not need to be written into legally binding regulations.
But minister for disabled Esther McVey said on Thursday: "I know that disabled people and their representatives feel strongly that this important concept is set out in law and I am happy to do this."
She added: "Our intention has always been the same - we want to target support at those who need it most.
"We have always said that we will not just look at whether individuals can carry out activities but also the manner in which they do so."
Critics of the government's changes say one third of disabled people live in poverty and an estimated 42% fewer people would be eligible for mobility allowance as a result.
In exchanges in the House of Lords last week, Crossbencher Baroness Grey-Thompson, a Paralympic gold medallist, criticised the government for its "lack of consultation with disabled people" about the proposals.
Fellow crossbencher Lord Alton has said the fact people will have specially adapted vehicles taken away from them had caused "widespread disbelief and considerable distress".
For ministers, Lord Freud conceded: "I have to accept that there was inadequate discussion of the changes and that there is inadequate understanding of them."

Leading by 37.2 seconds heading into the last stage, the Briton narrowly missed parked cars as he went off the road with under one kilometre left.
However, he managed to quickly regroup as he finished 13.8 seconds ahead of world champion Sebastien Ogier.
"I'm a lucky boy. I got caught out on a bump," said Citroen driver Meeke, 37.
"Certainly one way to finish a rally."
Hyundai driver Thierry Neuville finished third, 45.9 seconds behind Ford's Ogier.
Leading by 30.9 seconds after bossing the first two days, Meeke won Sunday's penultimate stage to extend his lead to 37.2 seconds.
That left him having to negotiate the final 21.94km stage around Derramadero.
The county Tyrone man's late mishap left him only seventh fastest on the final stage but it proved enough to clinch a crucial victory following his disappointing performances in the opening two events of the season.
After being strongly fancied to contend for this year's title, Meeke crashed out in Monte Carlo and could only finish 12th in Sweden after another mistake.
Meeke, who competed in the championship for the first time in 2011, earned his first WRC win at Rally Argentina in 2015 and took further victories in Portugal and Finland last year.
The Northern Irishman's gamble of opting for hard compound tyres on Saturday's nine stages despite the threat of rain was crucial to his victory as he extended his lead to take firm control of the event.
Regulations governing eligibility for benefits for disabled people will be changed after criticism of their likely impact, the government has announced.
[NEXT_CONCEPT]
Northern Ireland's Kris Meeke survived a late scare at Rally Mexico to clinch his fourth win in a World Rally Championship event.