The evidence showed that in the months before the 2016 election, Mr. Stone strove to obtain emails that Russia had stolen from Democratic computers and funneled to WikiLeaks, which released them at strategic moments timed to damage Hillary Clinton, Mr. Trump’s Democratic opponent. “Every chance he got,” prosecutors said, Mr. Stone briefed the Trump campaign about whatever he had picked up about WikiLeaks’ plans.

But he told the House committee in September 2017 that he never described to anyone involved in the Trump campaign his conversations with an intermediary to WikiLeaks.

The trial called into question Mr. Trump’s own answers to queries from Mr. Mueller. The president, who refused to be interviewed and agreed to respond to questions only in writing, said he could not recall the specifics of any of 21 conversations he had with Mr. Stone in the six months before the election.

In one of the trial’s most revealing moments, Mr. Gates recounted a July 31, 2016, phone call between Mr. Stone and Mr. Trump, just days after WikiLeaks had released a trove of emails embarrassing the Clinton campaign. As soon as he hung up with Mr. Stone, Mr. Gates testified, Mr. Trump declared that “more information” was coming, an apparent reference to future releases from WikiLeaks that would rattle his political rival.

Within minutes of the verdict, Mr. Trump protested on Twitter that it was unfair. “So they now convict Roger Stone of lying and want to jail him for many years to come,” Mr. Trump wrote, though his own administration’s Justice Department prosecuted Mr. Stone.

He then listed the names of nearly a dozen favorite targets of his ire, including Mrs. Clinton, Mr. Mueller, the former F.B.I. director James B. Comey and Representative Adam B. Schiff, who heads the House Intelligence Committee. “Didn’t they lie?” he tweeted, and then added: “A double standard like never seen before in the history of our Country?”

Mr. Stone joins a notable list of former Trump aides who either pleaded guilty or were convicted of federal crimes in cases stemming from Mr. Mueller’s work. It includes Mr. Gates; Michael T. Flynn, the former national security adviser; Michael D. Cohen, the president’s longtime fixer; George Papadopoulos, a former Trump campaign aide; and Paul Manafort, Mr. Trump’s former campaign chairman and Mr. Stone’s onetime partner in a political consulting firm.