Justice Secretary Chris Grayling announced that fresh proposals for duty work - such as that picked up in police stations - will see a set number of contracts assessed on the quality and capacity of firms bidding for them.
Under the original proposals, price would have been a key factor.
A cap on the number of contracts to be awarded, which law firms feared could have closed 1,200 businesses, has also been lifted under the revised reforms.
The new proposals were drawn up following talks with the Law Society, which represents tens of thousands of solicitors.
Law Society president Nicholas Fluck welcomed the proposals as "a shared way forward for a more stable and sustainable criminal legal aid system".
Mr Fluck said: "The new proposals will demand considerable change, but offer genuine opportunities for those firms who wish to continue to provide these crucial legal services."
Under the new draft proposals, legal aid is to be slashed for prisoners, foreigners and the wealthy in a move which could help the Government save £220 million a year.
Defendants with an annual disposable income of £37,500 a year and at least £3,000 to spare each month after paying essential bills would no longer receive automatic legal aid.
Mr Grayling said: "This Government is on the side of people who work hard and want to get on in life.
"We have an excellent tradition of legal aid and one of the best legal professions in the world. But we cannot close our eyes to the fact legal aid is costing too much.
"I have listened to lawyers' concerns and had constructive discussions with the Law Society.
"They acknowledge that, whilst it may be difficult, change is also inevitable. But it must be the right change that brings about the right outcomes.
"The proposals we have agreed make sure legally-aided lawyers will always be available when needed and that people can choose the lawyer they want to help them."
Barrister-turned-MP Karl Turner raised fears earlier that price-competitive tendering for legal aid would allow multinational firms to provide justice at the cheapest cost.
The Labour MP told MPs he believed it would lead to private companies such as G4S and Serco dominating the legal aid market at the expense of smaller firms that possess greater expertise.
Rachel Robinson, policy officer for rights organisation Liberty, said: "This is our criminal justice system, not the budget airline market, so credit to the Lord Chancellor for dropping plans for price competitive tendering and improving flat-fee proposals.
"Exemptions for the vulnerable from the residency test are welcome but must go further and, with the judicial review's future uncertain, the fight for fairness goes on."