Parliament must debate as early as possible after the expected election whether terminally ill patients should be given the right to die, peers say.
Some countries allow assisted dying but there is a ban in the UK
The House of Lords Select Committee was divided over whether the law should be changed.
But it said any future legislation must make a clear distinction between assisted suicide and euthanasia.
The report marks a shift from the last parliamentary inquiry in 1994, which recommended no change.
Committee chairman Lord Mackay of Clashfern said: "Ending or helping to end someone's life, albeit with their consent, is an awesome issue, and opinion within the committee has been divided."
He added he hoped the report would "inform future debate and improve public understanding of this complex and emotive subject".
The committee was set up to look into Lord Joffe's assisted Dying for the Terminally Ill Bill, which proposes a lifting of the UK ban to "enable a competent adult who is suffering unbearably as a result of a terminal illness to receive medical assistance to die at his/her own considered and persistent request".
The committee accepted the bill was not going to become law - parliament is likely to be dissolved within days for the forthcoming election.
But the peers said their report should be debated early in the next parliament.
It recommended that if a future bill was brought before MPs, it should clearly differentiate between assisted suicide, whereby medics provide the means for a patient to kill themselves, and voluntary euthanasia, when a patient is too ill to administer the lethal medication, but consents to someone else doing it.
The peers looked at two other countries which had introduced right to die legislation.
In Holland, assisted suicide and voluntary euthanasia are responsible for one in 40 deaths.
Whereas, one in 700 deaths in the US state of Oregon are from assisted suicide - voluntary euthanasia is not allowed.
The peers heard that doctors, who are generally not in favour of allowing patients the right to die, were more likely to support assisted suicide.
The committee warned that when patients had to take their own life, they were forced to think more carefully about the move than when someone else had the responsibility.
The report also said terminal illness had to be strictly defined, and doctors should not have to assist a patient if they had a conscientious objection.
Lord Joffe said he would be introducing a new bill in the next parliament, once the committee's report had been debated.
He said: "I believe the problems and the suffering caused by the present laws will become increasingly difficult for parliament to ignore."
A spokesman for the Voluntary Euthanasia Society said: "This is a momentous day for terminally ill patients who want greater choice at the end of their lives.
"The report is a green light for a change in the law and we look forward to a new bill being reintroduced into the Lords as a matter of urgency."
And Liberal Democrat MP Dr Evan Harris, a former hospital doctor, said the report was welcomed, adding "It's about time the political establishment shifted away from their comfortable position of rejecting any change in the law and closing down debate."
But Julia Millington, of the ProLife Party, said there was no need for a change in the law and if anything it should be reinforced.
She also said: "We dispute the need for any further debate on the subject."