In his decree appointing Ghaani, Khamenei characterized him as "one of the most distinguished Revolutionary Guard commanders", the Persian-language Radio Farda said in a report.
The Quds Force, which is part of the 125,000-strong Iran's Islamic Revolution Guards Corps (IRGC), is a paramilitary organisation that answers directly to Khamenei.
Ghaani fought in the Iran-Iraq War of the 1980s and was a close and trusted aide to Soleimani.
He also served as an intelligence official in the Iran's Islamic Revolution Guards Corps (IRGC).
According to the Radio Farda report, Ghaani is known for his extremist opposition to Israel, similar to Soleimani, and was one of the key figures in Iran's involvement in the Syrian civil war.
However, unlike Soleimani who usually refrained from commenting on internal political issues, Ghaani had no reservations to intervene and express his views.
The January 3 airstrike, which was ordered by US President Donald Trump, hit Soleimani's motorcade near the Baghdad International Airport.
A total of 10 people were killed, including the Iran Major General and Abu Mahdi al-Muhandis, the second-in-command of Iraq's Popular Mobilization Front (PMF).
Khamenei and President Hassan Rouhani have vowed to retaliate against the US over Soleimani's death.
The airstrike came after Iraqi protesters on December 31 stormed the US embassy compound in Baghdad to protest the American air raids conducted on December 29 against five bases of Iran-backed militias in Iraq and Syria, claiming the lives of 25 people.
( With inputs from IANS )