Career diplomat Deborah Jones will present her credentials tomorrow to the General National Congress, Libya's highest political and legislative authority, state news agency LANA said.
Jones succeeds Chris Stevens, a popular figure among the Libyan people, who was killed along with the other three when Islamists overran the Benghazi mission and a nearby CIA annexe on September 13.
Despite a Libyan and FBI-led investigation, no one has been charged with the killings. The incident, just weeks before President Barack Obama was re-elected, remains a political football, with Republicans accusing the administration of a cover-up.
From 2008 to 2011, she was ambassador to Kuwait, and has been working at the Middle East Institute in Washington since then.
At her swearing-in last week, she acknowledged it would take time for democracy to take firm hold in Libya, but praised the Libyan people's commitment to such ideals.
"The Libyan people endured 42 years of rule by intimidation. They courageously defeated a dictator and are now determined to experience governance by representation," she said, referring to long-time dictator Muammar Gaddafi, ousted in 2011.