Ukrainian troops have been greeted by joyous residents in the centre of Kherson after Russia abandoned the only regional capital it had captured since its invasion in February.

Russia said it had withdrawn 30,000 troops across the Dnipro River without losing a single soldier but Ukrainians painted a picture of a chaotic retreat, with Russian troops ditching their uniforms, abandoning weapons and drowning while trying to flee.

Video footage verified by Reuters showed dozens of Ukrainians cheering and chanting victory slogans in Kherson’s central square, where the apparent first Ukrainian troops to arrive snapped selfies in the crowd.

Two men lifted a female soldier on their shoulders and tossed her into the air.

Some residents wrapped themselves in Ukrainian flags.

One man was weeping with joy.

A Ukrainian female soldier poses for a photo against a Kherson sign in the background, in Kherson, Ukraine.  Photo: AAP

Ukraine’s defence intelligence agency said Kherson was returning to Ukrainian control and ordered any remaining Russian troops to surrender to Ukrainian forces entering the city.

Locals had placed Ukrainian flags in the square as news of the end of more than eight months of occupation filtered out.

“Glory to Ukraine! Glory to the Heroes! Glory to the Nation!,” one man shouted in another video verified by Reuters.

As Ukrainian forces surged forward during one of the most rapid and humiliating Russian retreats of the war, villagers came out of hiding to describe how Russian troops had killed residents and looted homes.

At the newly recaptured village of Blahodatne reached by Reuters 20km north of Kherson, Ukrainian soldiers were taking over positions dug by the Russians.

At the entrance of the village, Ukrainian troops looked over a large stockpile of 120mm mortar shells abandoned by Russian forces in a dilapidated warehouse.

Defence and Security Analyst Professor Michael Clarke told Sky News what looks like a collapse of Russia’s forces in Kherson is dramatic and humiliating.

“This is the only significant city the Russians took in February, and now they’ve lost it,” he said.

Serhiy Khlan, a member of Ukraine’s regional council for Kherson, said the regional capital was now almost fully under the control of Ukrainian forces.

A large number of Russian soldiers had drowned in the river trying to escape and others had changed into civilian clothing, he said, advising residents not to leave their homes while searches for remaining Russian troops took place.

Natalia Humeniuk, a spokeswoman for the Ukrainian military’s southern command, said “saboteur operations cannot be ruled out” by Russian troops in civilian clothes.

Earlier, the Russian defence ministry said it had finished its withdrawal from the western bank of the Dnipro river, where Kherson city lies, two days after Russia announced the retreat.

“Not a single unit of military equipment or weapons have been left on the right (western) bank. All Russian servicemen crossed to the left bank,” it added, saying that Russia had not suffered any loss of personnel or equipment.

Pro-Russian war bloggers had reported late on Thursday that Russian forces crossing the river were coming under heavy fire from Ukrainian forces.

The Russian ministry said Ukrainian forces had struck Dnipro River crossings five times overnight with US-supplied HIMARS rocket systems.

Ukraine’s advance unfolded far more rapidly than Ukrainian officials had suggested just hours earlier.

Defence Minister Oleksii Reznikov had told Reuters on Thursday it would take at least a week for Russia to pull out of Kherson.

He estimated Russia still had 40,000 troops in the region and said intelligence showed its forces remained in and around the city.

“They managed to scarper, the scum,” Oleksiy Arestovych, an advisor to President Volodymyr Zelenskiy, tweeted.

“There are not many prisoners, mainly losses. But trophies enough.”

Kherson province is one of four that Russian President Vladimir Putin claimed to have annexed from Ukraine in late September.

The Russian defence ministry said it had adopted “defensive lines and positions” on the eastern bank of the river, which Russia hopes it will be able to better supply and defend.

Putin’s spokesman Dmitry Peskov said the decision to retreat was taken by the defence ministry.

Asked by reporters if it was humiliating for Putin, Peskov said: “No.”

Ukraine’s president Volodymyr Zelensky hailed the progress in an address on his official website.

“Today is a historic day. We are regaining the south of our country, regaining Kherson,” he said.

— with AAP