The move followed a week in which the White House was thrown into uproar after Trump fired FBI Director James Comey, Reuters said.
Democrats and some of the president's fellow Republicans had demanded an independent probe of whether Russia tried to sway the outcome of November's election in favor of Trump and against Democrat Hillary Clinton.
Trump, whose anger over the allegations has grown in recent weeks, took the news calmly and used it to rally his team to unite, move on and refocus on his stalled agenda, a senior White House official said.
"We are all in this together," Trump told his team, the official said.
Trump said in a statement after the Justice Department announcement he looked forward to a quick resolution.
"As I have stated many times, a thorough investigation will confirm what we already know - there was no collusion between my campaign and any foreign entity," he said.
Mueller said in a statement tweeted by CBS News: "I accept this responsibility and will discharge it to the best of my ability."
Read alsoNYT: Comey memo says Trump asked him to end Flynn investigationTrump, who said in a speech earlier on Wednesday that no politician in history "has been treated worse or more unfairly," has long bristled at the notion that Russia played any role in his election victory.
The Russia issue has, however, clouded his early months in office. Moscow has denied the conclusion by U.S. intelligence agencies that it meddled in the campaign.
Read alsoFired FBI director willing to testify, but only in public - mediaPressure on the White House intensified after Trump fired Comey, who had been leading a federal probe into the matter, and allegations that Trump had asked Comey to end the FBI investigation into ties between Trump's first national security adviser, Michael Flynn, and Russia. That raised questions about whether the president improperly attempted to interfere with a federal investigation.
The issue spilled over onto Wall Street on Wednesday, where the S&P 500 and the Dow had their biggest one-day declines since September as investor hopes for tax cuts and other pro-business policies faded amid the political tumult. The Justice Department announcement came after the market close.
INNER CIRCLE
"My decision (to appoint a special counsel) is not the finding that crimes have been committed or that any prosecution is warranted. I have made no such determination," Deputy Attorney General Rod Rosenstein said in a statement announcing the special counsel.
"I determined that a special counsel is necessary in order for the American people to have full confidence in the outcome," he said.
Trump heard about Mueller's appointment from his White House lawyer Don McGahn about 25 minutes before it was made public, the senior White House official said.
Trump assembled his inner circle in the Oval Office - Vice President Mike Pence, chief of staff Reince Preibus, economic adviser Gary Cohn, senior strategist Steve Bannon, and others - and gave them a pep talk, dictating the statement that was soon released.
Trump told them the appointment would allow them to refer questions to Mueller, giving them space to focus on policies such as tax reform.
Lawmakers on Capitol Hill generally welcomed the Justice Department action and praised Mueller for his integrity, but House and Senate Republican leaders said they would go on with their own investigations of the Russia matter.
