In a statement, the IRGC said that Abu Mahdi al-Muhandis, the second-in-command of the Hashd Shaabi or the Iraqi Popular Mobilization Forces (PMF), was also killed along with Soleimani in the strikes that targeted their vehicle on the Baghdad International Airport road, the Tehran-based Press TV reported.
The PMF has also confirmed the incident.
"The deputy head of the Hashd, Abu Mahdi al-Muhandis, and head of the Quds Force, Qassem Soleimani, were killed in a US strike that targeted their car," it said in a statement on Friday.
The group had earlier said that its public relations director Mohammed Reza al-Jaberi and four other members were also killed after three Katyusha rockets struck a military base next to the Baghdad airport earlier on Friday.
The PMF described the attack as a "cowardly US bombing".
Meanwhile, the Pentagon said that Soleimani was killed "at the direction of the President".
"At the direction of the President, the US military has taken decisive defensive action to protect US personnel abroad by killing Qasem Soleimani," the BBC quoted a Pentagon statement as saying.
"This strike was aimed at deterring future Iranian attack plans. The US will continue to take all necessary action to protect our people and our interests wherever they are around the world."
The strike comes days after protesters surrounded the US embassy in Baghdad, clashing with American forces at the scene.
US Defence Secretary Mark Esper said late on Thursday that Washington would not accept attacks against its personnel in the region, blaming Iran for the violence at the embassy.
Since 1998, Maj Gen Soleimani has led Iran's Quds Force - the IRGC's elite unit which handles clandestine operations abroad, said the BBC.
In that position Gen Soleimani played a key role bolstering Bashar al-Assad's Iranian-supported government in the Syrian Civil War, and in the fight against the Islamic State (IS) group in Iraq.
He was a hugely significant figure in the Iranian regime. His Quds Force reported directly to Supreme Leader Ayatollah Ali Khamenei.
He first came to prominence in his country serving in the Iran-Iraq War in the 1980s.
( With inputs from IANS )