Unger, a Republican, joins Democrats Isaac Hunt and Paul Carey on the three-member panel.
The appointment of the 40-year-old as an interim chairman was expected while Bush seeks a permanent replacement whose appointment must be ratified by the US Senate.
Unger has served as a commissioner of the SEC since 1997 and is best-known for championing the role of technology in the financial markets.
Levitt, 69, was the longest-serving chairman in the history of the SEC having been appointed by President Clinton in July 1993 and re-appointed for a second term in 1998. His term was due to end in 2003.
Last year he was at the forefront of accounting news, following his crusade for a new set of regulations ensuring auditor independence to safeguard investor confidence in financial reporting.
Likely contenders for the position full-time include Washington-based lawyer James Doty, Pfizer chairman William Steere and Republican congressman Christopher Cox. The process of choosing the 26th SEC chairman is expected to last several months.
A new head of solutions, Aidan Brennan, has been appointed at KPMG UK
The second largest improvement in ‘significant’ levels of financial distress since the EU Referendum was in professional services, found research from Begbies Traynor
Just one half of UK practices have implemented a pricing structure around auto enrolment implementation and advice - with many suffering increased costs
Deloitte's north-west Europe foray; BDO, Smith & Williamson investment paths; Shelley Stock Hutter; and Wilkins Kennedy discussed by editor Kevin Reed on our Friday Afternoon Live broadcast