Cohen was ordered to report to the Otisville federal prison — located some 75 miles northwest of New York City — no later than 2:00 p.m., NBC News reported.
"There still remains much to be told, and I look forward to the day that I can share the truth," Cohen told reporters earlier on Monday.
The Otisville prison is comprised of two federal facilities — a medium-security prison and a satellite campus for non-violent offenders like Cohen. The facility houses 800 inmates.
Last year, Cohen was sentenced to three years in prison for lying to Congress, fraud, tax evasion and making unlawful campaign contributions, including "hush money" payments to women who claimed they had relations with Trump.