Salam, the son of a former prime minister, said he would work to form a "government of national interest," The (Beirut) Daily Star reported.
His appointment was agreed to by 124 of the 128 members of Parliament and had the backing of Hezbollah.
The last government resigned two weeks ago over disagreements about the June elections, the BBC reported.
Salam is the son of late Prime Minister Saeb Salam.
Celebrity Families of 2014 [PHOTOS]