Kenneth Clarke said funding will be axed for a wide range of disputes, including those over relationship break-ups, school admissions and expulsions, as well as clinical negligence in a bid to save £350 million over the next four years.
But asylum cases, mental health cases and debt and housing matters where someone's home is at immediate risk will all still be funded.
Mr Clarke told MPs there was a "compelling case for going back to first principles in reforming legal aid".
"It cannot be right that the taxpayer is footing the bill for unnecessary court cases which would never have even reached the courtroom door, were it not for the fact that somebody else was paying," he said.
The importance of the case, the ability of those involved to present their own case and the availability of other sources of funding or other routes to resolve the issue were all considered in the review, he said.
"I propose to introduce a more targeted civil and family scheme which will discourage people from resorting to lawyers whenever they face a problem, and instead encourage them to consider more suitable methods of dispute resolution."
But he added: "Legal aid will still be routinely available in civil and family cases where people's life or liberty is at stake, or where they are at risk of serious physical harm, or immediate loss of their home."
The scope of criminal legal aid will remain the same.
Announcing a fundamental rethink of the £2.1 billion-a-year scheme, Mr Clarke said: "We propose to remove from the scope of the scheme issues which are not, generally speaking, of sufficient priority to justify funding at the taxpayer's expense."
At present, anyone with assets worth less than £8,000 qualifies - with those worth up to £3,000 paying nothing and others expected to make a contribution.
Under the new system, anyone with assets worth more than £1,000 will have to pay at least £100 towards their legal costs.
Civil legal aid will be axed for cases involving divorce, employment, clinical negligence, and personal injury as well as immigration where the individual is not detained, welfare benefits and school exclusion appeals, Mr Clarke said.
But funding will still be available for prisoners to make claims for gross negligence, claims against public authorities, community care, domestic violence and debt matters where a home is at risk, among others.
Funding for private family law cases will be axed in a move that could save £178 million per year.
Exceptions will be made for those cases that involve domestic violence, forced marriage or child abduction, Mr Clarke said.
Funding will still be available for mediation as a means to resolve disputes, he added.
Civil legal aid for clinical negligence cases will also be axed, with those involved encouraged to seek other sources of funding, including so-called "no win, no fee" arrangements.
But the no win, no fee conditional fee arrangements (CFAs) will also be reformed to cut the "spiralling costs" involved.
"The key proposal is to abolish recoverability of success fees and the associated after the event insurance premiums," Mr Clarke said.
Claimants "should have to pay their lawyer's success fee and will therefore take an interest in controlling the costs being incurred on their behalf", he said.
"This will also reduce the disproportionate costs burden on defendants."
Mr Clarke went on: "Taken together, my reform proposals complement the wider programme of reform which I will be bringing forward to move towards a simpler justice system."
The new system will be "more responsive to public needs" and allow "people to resolve their issues out of court, using simpler, more informal remedies where they are appropriate, and which encourages more efficient resolution of contested cases where necessary".
Fees paid in civil and family cases will be cut "by 10% across the board", with similar cuts in experts' fees, Mr Clarke said.
He also announced plans to introduce a single fixed fee for a guilty plea, based on fee rates in magistrates' courts.
The same fee should be paid in respect of a guilty plea in the crown court, "regardless of the stage at which the plea is entered", he said.
The move is part of plans to "contain" the costs of the most expensive criminal cases.
Many of the cases in which civil legal aid will be scrapped involve issues "which are not necessarily of a legal nature but require other forms of expert advice to resolve", the Ministry of Justice said.
Telephone support services will be extended to help meet this need.
The disability charity Scope said it was "difficult" to see "how the reforms will allow disabled people to better hold decision-makers to account for their actions".
Chief executive Richard Hawkes said: "The benefit system is notoriously complex and prone to administrative error.
"In an era of budget cuts, job losses and welfare reform that contains some pretty sharp sticks, what now happens to disabled people who fall foul of public and private bureaucracies?
"The courts have traditionally been the last line of defence against poor, unfair and unlawful decisions."
Blair Gibbs, head of the crime and justice unit at the Policy Exchange think-tank, added: "The cost drivers of our system - such as our complex adversarial court process, high crime rates, the Human Rights Act and a growing litigation culture - will not go away.
"That means fundamental reform is required to make the system fit for the long term.
"In addition to taking large amounts of claimants out of scope, there needs to be a plan for what happens once the State withdraws.
"We should be looking at ways of bringing new money into the system, including more use of before-the-event insurance, and asking people to pay extra if they want expensive add-ons such as expert witnesses and the finest legal brains in the land."
