The United Nations Security Council has voted to lift more than a decade of sanctions against Libya.
The bombing of Flight 103 in 1988 killed 270 people
The move clears the way for the payment of compensation to families of the victims of the bombing of a Pan Am jet above the Scottish town of Lockerbie in 1988.
Libyan state radio hailed the vote as a "victory" which opened a "new page" in Tripoli's drive to normalise relations with the West.
France had threatened to oppose the draft resolution, but abstained in the vote after Libya agreed to increase compensation payments to relatives of those who died when a French airliner was bombed over Africa in 1989.
There were 13 votes for the draft resolution, none against, and two abstentions - the other being the US which was set to maintain its own separate sanctions on Libya.
Imposed in 1992 and 1993
Forbade aircraft movements to or from Libya unless UN approved
Banned sale of aircraft equipment/parts
Halted operation of Libyan Arab Airlines office abroad
Banned sale of arms, military equipment
Limited diplomatic staff in Libya
Froze Libya's assets abroad
Banned sale of oil-related equipment
Suspended in 1999
"The United States continues to have serious concerns about other aspects of Libyan behaviour," James Cunningham, the deputy US
ambassador to the Council, said.
UK Foreign Secretary Jack Straw welcomed the "result of patient but firm diplomacy".
"This is a result of Libya doing what the Security Council has demanded: accept responsibility for the horrendous Lockerbie bombing in 1988...; renounce terrorism; pay compensation; and undertake to co-operate with any future Lockerbie investigation."
BBC News Online world affairs correspondent Paul Reynolds says the lifting of UN sanctions means that Libya has largely, though not wholly, emerged from its long period of international isolation.
The sanctions - a ban on flights and sales of some oil equipment and the freezing of some Libyan assets - were suspended in 1999 when Libya handed over two suspects in the Lockerbie bombing.
Their formal removal will help Libya's new policy of trying to repair its external relations, our correspondent adds.
Libya called for all nations to open a dialogue with Tripoli, and said it was "committed to world peace".
Libya's leader is keen to secure foreign investment in Libya
Mohammad al-Zuai, the official in charge of the Lockerbie
negotiations, said: "We welcome the Security Council decision, which shows that Libya has kept all its promises and respects international law and legality".
Libya has agreed to pay $2.7bn in damages to relatives of the Lockerbie victims, but the sum was considerably more than the $34m paid to victims of the downed French plane in 1999.
Embarrassed, France threatened to veto the resolution at the UN unless Libya revised the settlement figure.
Judicial claims 'dropped'
After negotiations, Libya reportedly offered to pay up to an additional $1m to the French families.
Libya has never accepted responsibility for the downing of the UTA flight above Niger which claimed 170 lives, but agreed to pay compensation after a Paris court convicted six Libyans of the bombing in absentia.
The compensation agreement will mean France drops all judicial claims against Libyans, Libya's official news agency Jana reported.
The BBC's David Bamford says there is a sense of relief in Washington that the last-minute intervention by the French Government did not throw the negotiated deal with Libya completely off course.
France has done itself no favours as far as American public opinion is concerned, particularly in the wake of its stringent opposition to US policies in Iraq, our correspondent says.
The UN sanctions were imposed in the early 1990s to pressure Libya into handing over two men suspected of involvement in the Lockerbie bombing.
They were suspended in 1999 after Libya handed over the two suspects for trial.