"I now have significantly greater confidence that the investigation will follow the facts, wherever they lead," said Senate Majority Leader Sen. Charles Schumer (D-NY).
"The appointment of Bob Mueller as special counsel for the Russia investigation is a good first step to get to the bottom of the many questions we have about Russian interference in our election and possible ties to the president," said Sen. Dianne Feinstein (D-CA).
"Mueller has a strong reputation for independence, and comes with the right credentials for this job," said Sen. Charles Grassley (R-IA).
"This was a necessary and long overdue step by the Department of Justice," said Rep. Tim Ryan (D-OH).
Democrats had sternly criticized Rosenstein for not making that appointment last week, especially in the aftermath of the firing of Comey by President Donald Trump.
"Mueller has a distinguished career as both a prosecutor & director of the FBI," said Rep. Trey Gowdy (R-SC) on Twitter. "I was always impressed with his integrity & even handedness."
Mueller took over as FBI Director just a week before the September 11, 2001 attacks; he was appointed by President George W. Bush, and served until 2013, when he was replaced by Comey.
"Mr. Mueller has unquestioned integrity and is a wise choice to lead the FBI investigation as Special Counsel," said Rep. John Faso (R-NY).
As for Republican leaders in Congress, both Speaker Paul Ryan and Senate Majority Leader Mitch McConnell indicated that investigations by House and Senate committees would still proceed, even with the Mueller choice.
The White House reaction was subdued.
"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," the President said in a written statement issued almost 90 minutes after the announcement.
"I look forward to this matter concluding quickly," the President said, adding that "I will never stop fighting for the people and the issues that matter most to the future of our country."
The announcement came as Mr. Trump was interviewing more candidates at the White House to replace Comey; published reports indicated that officials were informed after the decision was made.
Normally, the decision on a special counsel would have been for the Attorney General, but Jeff Sessions recused himself in early March, leaving that to the Deputy Attorney General.