"This is a very important agreement," Welch said after the signing ceremony, saying the deal "turns a new page in our relationship".
"This agreement signed today is designed to resolve the last major historical issue that has stood in the way of a more normal relationship between our two countries.
"Under this agreement each country's citizens can receive fair compensation for past incidents. When fulfilled, the agreement will permit Libya and the US to develop their relations."
US victims covered include those who died in the 1988 bombing of Pan Am Flight 103 over Lockerbie, Scotland, Libyan officials said.
The attack killed 270 people, while another on a Berlin disco in 1986 claimed three people and wounded 229.
The deal also covers Libyans killed in 1986, when US military aircraft bombed Tripoli and Benghazi - an attack in which 40 people died.
Ties between Libya and the US have improved dramatically since 2003, when Libya accepted responsibility for the Lockerbie bombing and said it would stop pursuing nuclear, chemical and biological weapons.
Since then, the US has dropped many sanctions against Libya, removed the country from a "terrorism blacklist" and restored diplomatic ties after decades of enmity.
But earlier this year Libya objected to new US legislation to enable victims of "terrorism" to collect damages from governments such as Libya by having their assets frozen.
The deal on Thursday resolves that dispute.
Jana, Libya's state news agency, published the text of the agreement, saying the "humanitarian fund" would rule on compensation claims.
Amounts to be paid and ways of doing so were also laid out but were not reported.
Jana said that George Bush, the US president, had sent a message to Muammar Gaddafi, the Libyan president, in which he expressed his "satisfaction" at the improvement in relations between Washington and Tripoli.
Both US houses of congress have passed a bill that grants Libya immunity from lawsuits once compensation has been paid through the fund.