A plane linked to Prigozhin and believed to be carrying him into exile landed in Belarus from the southern Russian city of Rostov early on Tuesday, a flight tracking service said.
The deal was negotiated by Lukashenko that ended the mercenaries' mutiny in Russia on Saturday. Russian President Vladimir Putin said Wagner's fighters would be offered the choice of relocating there.
In Moscow, President Putin praised Russia's armed forces for preventing a civil war as he sought to reassert his authority after the mutiny led by Prigozhin in protest against the Russian military's handling of the conflict in Ukraine.
Russian authorities also dropped a criminal case against his Wagner Group mercenary force, state news agency RIA reported, apparently fulfilling another condition of the deal brokered by Lukashenko late on Saturday that defused the crisis.
Prigozhin, a former Putin ally and ex-convict whose mercenaries have fought the bloodiest battles of the Ukraine war and taken heavy casualties, had earlier said he would go to neighbouring Belarus at the invitation of Lukashenko, a close Putin ally.
Putin meanwhile told some 2,500 security personnel mustered for a ceremony on a square in the Kremlin complex that the people and the armed forces had stood together in opposition to the rebel mercenaries.
"You have defended the constitutional order, the lives, security and freedom of our citizens. You have saved our Motherland from upheaval. In fact, you have stopped a civil war," he said.
Putin was joined by Defence Minister Sergei Shoigu, whose dismissal had been one of the mutineers' main demands.
Putin also requested a minute of silence to honour Russian military pilots killed in the revolt. The fighters had shot down several aircraft during their run towards Moscow, although they faced no resistance on the ground.
Putin also said on Tuesday that the finances of Prigozhin's catering firm would be investigated after his mutiny, saying Wagner and its founder had received almost $2 billion from Russia in the past year.
Prigozhin, 62, said he launched the mutiny to save his group after being ordered to place it under the command of the defence ministry.
His fighters had halted their campaign on Saturday to avert bloodshed after nearly reaching Moscow, and regretted being forced to shoot down aircraft on the way, he said.
Russian leaders have tried to convey that the situation is returning to normal after the aborted mutiny. Putin met on Monday night with the heads of security services, including Defence Minister Shoigu.
Latvia and Lithuania called on Tuesday for Nato to strengthen its eastern borders in response to expectations that Russia's Wagner private company will set up a new base in Belarus after its abortive mutiny at home.
'They'll squash you like a bug' - Lukashenko says he talked Prigozhin out of march on Moscow
Belarusian President Alexander Lukashenko on Tuesday said his country has not been building camps for exiled mercenaries of the Wagner Group. According to Lukashenko, he offered them an abandoned military base where they could erect their tents.
Lukashenko also explained his motivation for taking part in talks around the mutiny in Russia.
According to him, the troubles in Russia could spread to Belarus. "If Russia falls, we will be buried under the wreckage", he told the assembled military personnel in his palace.
Belarus leader shared his take on talks with Wagner Group chief Yevgeny Prigozhin on Saturday as mutinous members of the private military company marched on Moscow.
According to Lukashenko, it was he who managed to talk Prigozhin out of trying to enter Moscow, warning him his units would be "squashed like a bug".
Lukashenko also said that he tried to convince Prigozhin that his desire for Russian President Vladimir Putin to hand over to him both Russian Defence Minister Sergei Shoigu and the General Chief of Staff of the Russian Army Valery Gerasimov would never happen.
"You know Putin as well as I do," Lukashenko quipped, adding that both Prigozhin and Shoigu shared similar fiery tempers.
Belarusian President said that his country wanted to learn from the war experience of Russia's Wagner mercenary group, the state-run Belta news agency reported.
Speaking to Belarus military in Minsk, Lukashenko said he put the Armed Forces on full combat alert and was ready to send a brigade to Russia to help Putin to stop the Wagner mutiny led by their leader Yevgeny Prigozhin.
He also recalled his call with the Russian president, Vladimir Putin, in which he said he had offered to try to strike a deal with Prigozhin.
While part of Wagner's forces is said to be moving to Belarus, Lukashenko suggested his military could pick up some of the mercenaries' combat experience obtained in Ukraine and elsewhere.
"If their commanders come to us and help us... tell us what's important right now... That's priceless. That's what we need to take from Wagner," Lukashenko said, adding there was no need for Belarus to fear the presence of the mercenaries. "We will keep a close eye on them."
Reuters