Siniora, a former finance minister, arrived at the presidential palace on Thursday, shortly after Lahoud completed consultations with parliament members to name the new premier. Of the 128 legislators, 126 nominated Saniora for the job.
Siniora was finance minister in five governments headed by Rafiq al-Hariri between 1992 and 2004.
Siniora, also a veteran banker and long time close aide of Rafiq al-Hariri, became the front-runner when he was nominated by the biggest bloc - the Future Movement - in the new parliament.
"The Future Movement has decided to name ... Fuad Siniora ... to pursue the reforms and the development process put in motion by the martyr Rafiq al-Hariri," a statement from the group had said.
The movement is now led by Saad al-Hariri, whose father Rafiq was killed on 14 February in a huge car bomb explosion in Beirut that plunged Lebanon into political turmoil.
Pro-Syrian Lahoud, who is himself facing calls to stand down, had earlier held consultations on the naming of the new prime minister on Thursday with the 128 members of the new parliament.
Under Lebanon's sectarian system, the post of prime minister is reserved for the Sunni Muslim community.
With its political allies, in particular backers of Druze leader Walid Jumblatt, the Future Movement was counting on at least 72 votes for its candidate.
On Tuesday, Lebanese MPs rhad e-elected a prominent pro-Syrian Shia as speaker at the inaugural session of the first parliament since the 1975-90 civil war not controlled by pro-Damascus factions.