WASHINGTON—Special counsel Robert Mueller concluded that President Trump and his campaign didn’t conspire or coordinate with Russia to interfere in the 2016 election, according to a letter Attorney General William Barr sent to Congress on Sunday that summarized the final report on Mr. Mueller’s investigation.

But Mr. Mueller didn’t draw a conclusion on whether Mr. Trump obstructed justice, according to Mr. Barr’s letter, noting the report neither finds that the president committed a crime nor exonerated him. In the absence of a determination from Mr. Mueller, Mr. Barr wrote, he and Deputy Attorney General Rod Rosenstein concluded that Mr. Trump’s actions didn’t reach the bar of a crime.

The announcement brings to an end an investigation that has roiled the administration since 2017 when Mr. Trump fired James Comey, his Federal Bureau of Investigation director. But a new political drama over the report was set to begin, with congressional Democrats promising to investigate the report’s conclusions and seek access to the full document.

Mr. Trump—who has issued repeated attacks on the investigation and the lawyers and FBI agents involved—embraced the report’s findings. Speaking to reporters in Florida, Mr. Trump called the findings a “complete and total exoneration.” One of Mr. Trump’s attorneys, Rudy Giuliani, described the report as “better than I expected.”

Mr. Barr provided the details in a four-page letter summarizing the findings of the 22-month investigation. The special counsel “did not establish that members of the Trump campaign conspired or coordinated with the Russian government in its election interference activities,” Mr. Barr told Congress, quoting the report.