Another official told Channel 10 News that Mr Abramovich submitted a citizenship request "like any other person" with Israel's Moscow embassy and was accepted. The newspaper also reports that he is now Israel's richest citizen.
The Nativ Liaison Bureau, which facilitates immigration from Russian-speaking countries, said Abramovich applied for citizenship from overseas last week.
The Tier 1 investor visa that Abramovich has used to visit London regularly in recent years expired in April, and has yet to be renewed amid reports that United Kingdom authorities had demanded that he declare the source of his vast fortune as political tensions with Russian Federation escalate.
Joe Skipper Reuters Abramovich's little boat
Mr Abramovich is now in Tel Aviv but a spokesman would not comment on media reports that his citizenship had been granted.
Israel passport holders are allowed to enter Britain without a visa for short stays.
Thus, with a personal wealth of some 12.5 billion USA dollars, Abramovich has become Israel's richest national.
Mr Abramovich has been a regular visitor to Israel and Ynet said he had bought a property that was formerly a hotel. In Israel, meanwhile, he will be exempt from paying taxes and declaring income for ten years, under a controversial law that police reportedly say was pushed by Benjamin Netanyahu to benefit his billionaire friends in exchange for gifts. He has owned Chelsea since 2003.