Today's report says Hasan Rouhani named Eshaq Jahangiri, a former industry and mines minister, as First Vice President.
Jahangiri is a close ally of former reformist president Mohammed Khatami, who is disliked by hard-liners.
Iran has several vice presidents, but Jahangiri would be first in line of succession of anything were to happen to Rouhani.
Rouhani, who was primarily supported by reformists and centrists but who pledged to form a non-factional government, has also proposed several conservatives to his Cabinet.
Rouhani won a landslide victory in June presidential elections. He took the oath of office yesterday and sent his proposed Cabinet list to the parliament for a vote of confidence.