Immigration officials told the BBC that he was interviewed last week at the Israeli embassy in Moscow.
He has flown to Tel Aviv but a spokesman would not comment on media reports citizenship had been granted.
Mr Abramovich, 51, would be the richest person in Israel.
His UK investor visa reportedly expired some weeks ago but the British government has refused to comment on his individual case.
Mr Abramovich did not attend the FA cup final at Wembley earlier this month when Chelsea beat Manchester United.
Israeli media reports say he has been given an identity card in Israel under the Law of Return, which allows Jews to become citizens of Israel.
The Times of Israel said the interior ministry had confirmed Mr Abramovich arrived in Israel on Monday and that he had immigrated to the country.
He is a frequent visitor to Israel and bought a hotel in Tel Aviv in 2015 that reports say he has turned into a residence.
Israel passport holders are allowed to enter Britain without a visa for short stays.
Mr Abramovich is worth $11.5bn (£8.6bn), according to Forbes magazine.