Cohen, who once said he would "take a bullet" for Trump, was sentenced to three years in prison in 2018 for directing hush payments to pornographic film star Stormy Daniels and former Playboy model Karen McDougal, who claimed they had affairs with Trump.
Cohen began his sentence last May and was scheduled to be released from prison in November 2021. He will remain under quarantine for 14 days before he is released.
A judge denied a request by Cohen's on March 24 to have his sentence shortened. According to CNN, 14 inmates and seven guards at the facility where Cohen was serving his sentence tested positive for the virus.
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A March 30 statement on Cohen's Twitter page pointed out that infections had been confirmed at the upstate NY facility where he was being held.
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A lawyer for Cohen now says he will finish his sentence at home, United States media report.
Attorney General William Barr ordered the Bureau of Prisons earlier this month to increase the use of home confinement and expedite the release of eligible high-risk inmates, beginning at three prisons identified as coronavirus hot spots.
CNN first reported Cohen was being released to home confinement.
Spokespersons for the bureau and the USA attorney's office in Manhattan, which prosecuted Cohen, declined to comment.
Cohen, 53, was sent to a minimum-security camp at Otisville in upstate New York, about 110 km northwest of New York City.