The nomination continues a process that began when Muammar Gaddafi, the Libyan leader, took the surprise step of agreeing to end and dismantle his country's weapons of mass destruction programs.
The United States had not had formal diplomat relations with Tripoli since 1980, although a thaw in hostilities enabled Washington to open a diplomatic office in Libya in 2004.
Libya was held responsible for the bombing of Pan Am flight 103 over Lockerbie, Scotland, in 1988, which claimed 270 lives, most of them American.
Dec. 1979: Mob sets fire to US embassy in Tripoli
Feb. 1980: US ends ties, declares Libya state sponsor of terrorism
Apr. 1986: US jets bomb Libyan targets in retaliation for Berlin disco bomb
Dec. 1988: 270 people killed in bombing of Pan Am jet over Lockerbie, Scotland
Jan. 2001: Pan Am bomb suspects found guilty
Mar. 2003: Libya accepts responsibility for Lockerbie bombing and pays compensation to victims
Dec. 2003: Libya renounces WMD programmes
Sep. 2004: US ends trade embargo
May 2006: Bush announces restoration of full diplomatic ties
Gaddafi later agreed to pay $2.7bn in reparations to the victims' families.
However, several US senators are pressing the Bush administration to demand action from Gaddafi on unresolved compensation for the Lockerbie bombing.
They also want the administration to push for a complete Libyan accounting for a 1986 Berlin disco bombing that killed two US servicemen.
Unless the cases are settled, the senators said Congress may balk at state department requests for money for a new US Embassy in Tripoli, aid for Libya and senate confirmation of the new ambassador.
Throughout the 1980s, 1990s and early 2000s, Libya was regarded as a pariah state by Washington.
The country was designated a sponsor of terrorism, targeted by US airstrikes in 1986, and subjected to penalties barring American companies from doing business there.
But in May last year the Bush administration announced that it was resuming regular diplomatic relations with Libya for the first time in more than a quarter-century after removing Gadhafi's regime from a list of state sponsors of terrorism.