Berezovsky is an outspoken critic of Russia who lives in London but says he briefly fled abroad last month after a tip-off from police.
VIDEO: Plot revealed
He has accused Russian President Vladimir Putin of having ordered both his killing and the radiation poisoning of ex-agent Alexander Litvinenko.
London's Metropolitan Police confirmed they had arrested a man in the city centre on June 21 in connection with the alleged plot and handed him over to immigration authorities two days later.
The man was deported back to Russia, the force said, without confirming his nationality or age.
Alex Goldfarb, an associate of Litvinenko, told AFP the threat came on his widow Marina's birthday, June 16, as the pair returned from promoting their book on the case in Germany.
"I was supposed to meet Boris but when we landed at Heathrow we found out that he had to leave urgently on police advice," Goldfarb said.
They then went to exiled Chechen leader Akhmed Zakayev's house in London to celebrate Marina's birthday at a barbecue, where there were "tonnes" of uniformed and plain-clothes police.
Goldfarb — who left for New York the next day — said police told them the alert was due to "immediate threats" and Berezovksy had been told the same thing.
There was no confirmed link between the alleged plot to kill Berezovsky and the diplomatic row and Goldfarb could not shed any light on the identity of the alleged assassin.
But Berezovsky said he was convinced the Kremlin was involved as Goldfarb said the mood among Russian dissidents in London was "fatalistic."
"It's Putin personally behind this plot, Litvinenko and mine," Berezovsky told reporters in London, adding that he was "absolutely not surprised."
Russia's ambassador to London, Yuri Fedotov, told BBC radio that he was also not surprised that Berezovsky, a man Moscow accuses of corruption and other crimes, could be targeted but said any Kremlin role "is excluded."
Berezovsky gave no proof, but said only a state like Russia had the means to poison Litvinenko with radioactive polonium 210 and now it wanted to silence him because he was an "important witness" to his murder.
Repeating calls for a revolution in Russia, he added that he was now a target for assassination because of his ability to finance a "real opposition" movement that "can act" rather than just create noisy protests.
The reason the Russian government is trying so hard to block the
extradition of former KGB agent Andrei Lugovoi, whom British prosecutors accuse of poisoning Litvinenko, is in order to protect Putin himself, he charged.
The Russian exile called the press conference after The Sun newspaper reported that a hitman planned to execute him at the Hilton Hotel on London's Park Lane, next to Hyde Park, before it was foiled.
The Sun said Berezovsky's would-be assassin planned to lure him to a meeting while accompanied by a child in order to appear less suspicious.
Britain's security services MI5 and MI6 intercepted intelligence about the plot, but the hitman was seized before he could strike, the top-selling daily said.
The attack was to have taken place in the last two weeks, it added.
Berezovsky said he often holds meetings at the Hilton Hotel, because it is just three minutes from his office.
He also said that a source in Russia warned him of attempts against his life even before British police told him of the latest plot.
An assassin would visit London to meet with him and kill him openly, claiming it was over a business dispute.
Berezovsky, a close associate of late former Russian president Boris Yeltsin, obtained political asylum in Britain in 2003. London has repeatedly refused Moscow's request for him to be extradited to face fraud charges.
Moscow renewed an extradition request for Berezovsky after his call in April for "direct action" to oust Putin.
Berezovsky was among the first to point the finger at the Kremlin after Litvinenko, a friend and associate, fell violently ill on November 1 last year in London of what turned out to be poisoning from radioactive polonium.
He died three weeks later.