The change in leadership stems from an inspector general report that found the IRS inappropriately singled out conservative groups for enhanced scrutiny based on their names and political beliefs over an 18-month period during the 2012 campaign.
The FBI is investigating the matter, as are three congressional committees.
In his meeting with Werfel, the Utah Republican stressed that the IRS needs to make sure "strong safeguards are put in place to ensure there will be no targeting of individuals or groups based on political views."
Miller, who appeared before the Finance Committee on Tuesday, denied that the targeting was politically motivated. Rather he said it was a mistake by low-level workers trying to be more efficient.
The IRS sent letters to the targeted groups, in some cases demanding to know the names of current and future donors, political beliefs and any intention to run for office.
Political groups can become tax-exempt "social welfare" organizations if they spend less than half of their resources on public campaigns that don't promote or oppose specific candidates. The status allows these groups to keep their funders' identities secret.
None of the Utah tea party groups have claimed they were among those targeted, with local tea party leader David Kirkham saying he funded most of the gatherings to avoid the need to file for tax-exempt status with the IRS.
Freedom Path, a group created to support Hatch's 2012 re-election, says the IRS sent intrusive questionnaires and inappropriately gave ProPublica, an online media organization, its confidential application. The group spent at least $570,000 supporting Hatch. The senator's spokesman said the investigation is in no way connected to Freedom Path, but is a responsibility the senator has as the lead Republican on the committee overseeing the IRS.
Hatch asked Utahns who have information to go to www.hatch.senate.gov and fill out the online form, promising any data provided will remain private.