The IRGC said that Soleimani and Abu Mahdi al-Muhandis, the second-in-command of the Hashd Shaabi or the Iraqi Popular Mobilization Forces (PMF), were killed on Thursday night in a US airstrike that targeted the vehicle they were travelling in on the Baghdad International Airport road.
Responding to the development, Khamenei said that the "cruelest people on earth" assassinated the "honourable" commander who "courageously fought for year against the evils and bandits of the world", reports the Tehran-based Press TV.
"His demise will not stop his mission, but the criminals who have the blood of General Soleimani and other martyrs of the Thursday night attack on their hands must await a vigorous revenge.
"... The continued fight and achievement of the final victory will make life bitterer for the murderers and criminals," he added.
Besides offering condolences to Soleimani's family, Khamenei also declared three days of mourning.
The news of Soleiman's death was also confirmed by the Pentagon in a statement.
"At the direction of the (US) President, the US military has taken decisive defensive action to protect US personnel abroad by killing Qassem Soleimani," Efe news reported citing the Pentagon statement as saying.
"The 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," it added.
But in a tweet, Iranian Foreign Minister Mohammad Javad Zarif called the attack as "extremely dangerous and a foolish escalation", adding that "the US bears responsibility for all consequences of its rogue adventurism".
Mohsen Rezaei, the former commander of the IRGC, said Iran would take "vigorous revenge on America".
A spokesman for the Iranian government said the country's top security body would meeting in a few hours to discuss the "criminal act of attack".
Since 1998, Soleimani led Iran's Quds Force - the IRGC's elite unit which handles clandestine operations abroad and reports directly to Khamenei, 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 first came to prominence in his country serving in the Iran-Iraq War in the 1980s.
Thursday night's targeted strike took place amid increased tensions between Washington and Tehran after hundreds of protesters stormed the US Embassy in Baghdad on Tuesday, where they managed to breach the main gate and enter some rooms, lighting fires.
( With inputs from IANS )