“Never before have such unique and remarkable circumstances been presented to this court,” said Judge Juan M. Merchan, overseeing the case. “This was truly an extraordinary case.”

The judge then imposed a so-called unconditional release from Mr. Trump’s sentence, a rare and lenient alternative to prison or probation. Judge Merchan explained the leniency and confirmed Mr. Trump’s inauguration in ten days.

“Donald Trump, the ordinary citizen, Donald Trump, the criminal defendant” was not entitled to the protection of the presidency, Judge Merchan claimed, explaining that only the office protected him from the severity of the sentence.

The judge then wished Mr. Trump “good luck” and left the bench.

Mr. Trump appeared virtually, his scowl projected onto a screen in a cool but bright Lower Manhattan courtroom packed with reporters, cartoonists and court staff. He was at his Mar-a-Lago estate in Florida, sitting in front of two large American flags with one of his lawyers.

“This was a very terrible experience,” Trump said during the hearing, adding: “The fact is that I am completely innocent.”

He reiterated the primacy of the election over the verdict, saying voters could “see this firsthand.”

The hearing had begun with a senior prosecutor, Joshua Steinglass, summarizing the “overwhelming evidence” and saying that prosecutors had recommended so-called unconditional release for Mr. Trump.

But Mr. Steinglass still criticized Mr. Trump, saying that “far from expressing any kind of remorse for his criminal conduct, the defendant has intentionally fomented contempt for our institutions and the rule of law.”

Mr. Trump, he added, “has caused lasting damage to the public’s perception of the criminal justice system and put the court’s officials in danger.”

Mr Trump’s lawyer, Todd Blanche, said he “strongly disagrees” with Mr Steinglass. He criticized the legitimacy of the case and repeated Mr. Trump’s frequent claims that it was election interference.

He said it was a “sad day” for Mr Trump’s family – and the country.

Now that Mr. Trump has been convicted, he can formally appeal his conviction. However, he cannot forgive himself. The president’s pardon power does not extend to state charges.

The conviction follows Mr. Trump’s conviction for falsifying records to cover up a sex scandal that threatened to derail his primary campaign.

After the jury convicted Mr. Trump on all 34 counts in May, the former and future president fought tooth and nail to avoid the spectacle of a conviction.

Here’s what you should know about Mr. Trump’s conviction:

• The case: After a seven-week trial last spring, a 12-member New York jury convicted Mr. Trump of 34 counts of falsifying business records. The case arose in connection with a 2016 hush-money payment to a porn star, Stormy Daniels, who sold her story of a sexual encounter with Mr. Trump. Had she gone public, Ms. Daniels might have sparked a scandal in the final days of Mr. Trump’s 2016 campaign. The jury concluded that Mr. Trump reimbursed his fixer, Michael D. Cohen, for the hush money and then ordered records to be falsified to keep the payment secret.

• The punishment: Mr. Trump faced up to four years in prison, but his election victory made incarceration virtually and constitutionally impossible. And while a conditional discharge would have required Mr. Trump to meet certain requirements, such as maintaining employment or paying compensation, the unconditional discharge he is likely to receive has no conditions attached.

• A surprising decision: This month, Mr. Trump’s lawyers filed repeated motions in New York State Court to dismiss the case, all of which failed, leading to him asking the U.S. Supreme Court for an immediate stay. But the Supreme Court on Thursday rejected Mr. Trump’s request, a surprising display of independence from a court that has appeared to be sympathetic to Mr. Trump in other cases.