"I hope that when I rejoin my family and friends that the country will be in a place without xenophobia, injustice and lies at the helm," Cohen, 53, told a throng of reporters in Manhattan before departing for the federal prison in Otisville, New York, about 80 miles away.
"There's still much to be told, and I look forward to the day that I can share the truth," he added.
His brief comments suggested that he had not said everything about Trump during his many hours of testimony earlier this year before several congressional committees.
Cohen's lawyer, Lanny Davis, tweeted in support of his client Monday, saying "the truth has no walls."
Cohen pleaded guilty last year to arranging secret hush-money payments to two women who claim they had affairs with Trump years before he became president.
He also pleaded guilty to lying to Congress about details of an aborted plan to build a Trump Tower in Moscow, and to financial crimes.
Cohen told a federal judge in Manhattan that Trump had directed him to buy the silence of porn star Stormy Daniels and Playboy model Karen McDougal so they would not reveal in the months leading to the 2016 election their alleged trysts with the New York real estate developer years earlier.
Cohen directly paid off Daniels — and was later reimbursed by Trump — while the Trump-friendly publisher of The National Enquirer paid McDougal.
Trump has denied having sex with either Daniels or McDougal and has also called Cohen a liar.
Cohen, a former Trump Organization executive vice president, had been one of Trump's most loyal associates for years, and an attack dog when he faced unfavorable coverage from journalists.
He once said he would be willing to "take a bullet" for Trump.
But their relationship fell apart in the months after FBI agents raided Cohen's New York office and hotel room in April 2018, seizing evidence that led him to plead guilty.
Cohen eventually began cooperating with special counsel Robert Mueller's investigation of Russian interference in the 2016 election, possible collusion by Trump campaign officials in that meddling and possible obstruction of justice by Trump himself.
But the special counsel did not find evidence that Trump campaign officials coordinated with the Russians in their effort.
Attorney General William Barr has ruled that the evidence presented by Mueller did not warrant charging Trump with obstruction of justice.
Mueller did not say whether or not Trump should be charged with obstruction, but also said his report did not exonerate the president on that question.