Bush could announce the step as early as Monday, a senior administration official said on Sunday, speaking on condition of anonymity because Bush prefers to publicise such decisions himself.
The deadline for settlement with Muammar al-Qadhafi's government is Wednesday.
The official said the deal was not final until the formal announcement.
Bush has decided to end two sets of sanctions. The step would mark the latest reward from Washington for Libya's agreement last year to dismantle chemical, biological and nuclear weapons programmes.
High-level discussions on the final phase of Libya's disarmament pledges were held on Friday in London. Officials said the discussions were productive.
"This victory is thanks to more than two decades of tough multilateral sanctions and firm diplomacy sustained through Democratic and Republican administrations," said Congressman Tom Lantos, the ranking Democrat on the House International Relations Committee.
Lantos said that during his two visits to Libya this year, "it became clear to me that this decision is irreversible, and that the Libyan leadership has made a firm commitment to building new bridges to the United States and other civilised nations".
The 1998 bombing killed 259
people aboard Pan Am flight 103
The administration says Libya is to pay the new compensation after Bush agrees to lift both sanctions on air travel and a freeze on $1 billion in assets that belong to Libya or in which Libya has an interest.
Libya had insisted on a lifting of those sanctions as the price for the next compensation payments to families of the victims of Pan Am 103. The payment would come to $4 million for each family.
In the 1988 bombing, 259 people were killed on the plane - including 189 Americans - and 11 people in Lockerbie, the Scottish village on which parts of the Boeing 747 rained down.
Libya has acknowledged responsibility for the destruction of the Boeing 747.
The families have received one compensation payment of $4 million each thus far, part of a total compensation package of $10 million each. One family opted out of the agreement.
Still on the books are sanctions related to Libya's position on the US list of state sponsors of terrorism. If negotiations eventually lead to removal of those sanctions, Libya has said it would release a final compensation payment of $2 million for each family.
Bush had already eased a set of minor sanctions against Libya - imposed almost 20 years ago - earlier this month.