"There still remains much to be told, and I look forward to the day where I can share the truth".
Cohen was driven to the prison in a black SUV, arriving shortly after 11:30 a.m. (1530 GMT), some 2-1/2 hours before his deadline to report.
Trump has blasted Cohen, calling him a "rat" as well as a "bad lawyer and fraudster".
Cohen is the only person charged with a crime in connection with the hush-money payments to women who allegedly had affairs with Trump.
Cohen is headed to a prison about 75 miles north of NYC.
He is due to be held in the detention center's low-security "camp", which holds detainees who are not considered to be unsafe, including many other white collar criminals.
An MSNBC guest speculated Monday about Michael Cohen being the possible victim of violence in prison as he began his three-year stay there.
Cohen, 52, hinted he had more secrets to divulge as he made brief remarks to a crush of camera crews and reporters gathered on the sidewalk outside his Manhattan residence - the Trump Park Avenue apartment building - before being driven to the prison.
In February, Cohen testified before the House Oversight Committee about his role as Trump's fixer.
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If Cohen can't adjust, Donson said, "his time is going to be miserable". His case was referred to the Southern District of NY after being referred to prosecutors by special counsel Robert Mueller.
Mr. Cohen spent his last weekend of freedom with his family - and his last months unspooling the lurid story of his decade working at the Trump Organization, providing Congress and law enforcement a road map for possible further investigation.
With a menu that includes matzo ball soup and gefilte fish, as well as a full-time rabbi and a chance at the occasional visit home, the US prison where Donald Trump's former personal lawyer will spend the next three years is unique in the federal system.
Cohen also pleaded guilty to misleading Congress about his work on a proposal to build a Trump skyscraper in Moscow, hiding the fact that he continued to speak with Russians about the proposal well into the presidential campaign.
"[Bureau of Prisons] staff are trained and expected to conduct themselves professionally, including the humane and courteous treatment of the men and women in our custody", the Bureau of Prisons said in a statement.
The child of a Holocaust survivor and a nurse will become one of just two close aides of the president jailed for a lengthy period of time after Paul Manafort, Trump's ex-campaign manager who was sentenced to 7.5 years of prison.
His prison time could be reduced by about 15 percent for good behavior.
Cohen admitted to federal prosecutors that he helped arrange hush-money payments to buy the silence of porn actress Stormy Daniels and former Playboy model Karen McDougal in the run-up to the 2016 election.