The IRS scandal has prompted at least three congressional probes, as well as a criminal investigation by the Justice Department.
Obama fired the agency's acting director on Wednesday after an internal IRS watchdog found poor management led to an "inappropriate" focus on conservative groups.
Werfel has a track record of coolly responding to harsh questions from lawmakers. He testified multiple times this year about the damaging budget cuts that kicked in after Congress and the White House failed to reach a larger deficit reduction deal.
"The American people deserve to have the utmost confidence and trust in their government, and as we work to get to the bottom of what happened and restore confidence in the IRS, Danny has the experience and management ability necessary to lead the agency at this important time," Obama said in a statement.
"I have known Danny Werfel for more than 15 years," Treasury Secretary Jacob Lew said in a separate statement. "He is an immensely talented and dedicated public servant who has ably served presidents of both parties."
"Danny has a strong record of raising his hand for—and excelling at—tough management assignments," Lew added. "I am grateful to him for accepting this new challenge, and I am confident that his self-evident integrity and outstanding management skills will make an immediate difference in helping to restore public confidence in the IRS."
As the much-maligned agency faces withering scrutiny, IRS employees have pulled out of public events.
Lois Lerner, the head of the division that examines nonprofit claims, canceled plans to speak at a graduation ceremony for her law-school alma mater, Western New England University. The IRS softball team canceled a scheduled match with the office of Senator John Cornyn, the Texas Republican said on Facebook.
On Capitol Hill, the scandal seemed to rewind the clock to 2009 and 2010, when groups aligned with the conservative Tea Party movement were a frequent and vocal presence outside Congress.
At a rally that drew about 100 people from around the country, dozens of Tea Party leaders denounced the IRS and raised questions about the Obama administration's involvement.
"There is something profoundly un-American about targeting your political opponents," Kentucky Republican Senator Rand Paul, a potential 2016 presidential candidate, told the crowd.
Tea Party leaders described how the IRS prevented them from participating in the democratic process - in some cases by delaying their applications until after elections had passed, and in other cases through intrusive questioning that prompted some to give up their organizing effort altogether.
"The IRS just keeps asking questions. Our audit has been so intrusive," said Susan McLaughlin of the Liberty Tea Party in Liberty Township, Ohio. McLaughlin said her group had been waiting for three years to win tax-exempt status.
In the Senate, Republicans called on the IRS's internal watchdog to investigate whether the agency had leaked the donor list of the National Organization for Marriage, a conservative group fighting gay-marriage initiatives, to a rival group.
"This is what government intimidation and harassment looks like," Republican Leader Mitch McConnell said.
Other Republicans kept up the pressure as well.
House Speaker John Boehner accused the Obama administration of "remarkable arrogance" and said the scandal might lead to jail time for IRS officials, pointing to a law that mandates up to five years in prison for government officials found guilty of extortion or "willful oppression."
Republican Representative Darrell Issa said he wanted to question five IRS employees who may have played key roles in the scandal as his Oversight and Government Reform Committee looks into the matter.
Others said the net should be cast wider.
"The IRS low-level employees who made these egregious decisions need to be dealt with, but we also need to find out who directed them to do it and how high up does it go?" Republican Senator Rob Portman told Reuters.