Daley said Allison was "tough, always tells it like it is, and we look forward to his thorough and candid assessment."
The White House announcement came after a Republican-led Energy and Commerce subcommittee of the House of Representatives scheduled a meeting next week to decide whether to subpoena White House documents on Solyndra.
Energy Secretary Stephen Chu will also face a grilling before the committee next month.
President Barack Obama's Republican foes have been hunting for evidence that politics at the White House improperly shaped the Energy Department's decision to provide Solyndra with a US$535 million (NZ$650 million) loan guarantee.
The White House has denied acting inappropriately.
An official said that the probe conducted by Allison would last 60 days and would conclude with a public report to the administration that includes an evaluation of the current Department of Energy loan portfolio.
It will include recommendations on how to improve the system and establish an early warning system to identify concerns with managing the program.
Allison will also be authorised to bring in a team of outside experts to assist in the review of the portfolio and preparation of the report.
One report suggested that White House officials pressed for a decision on the loan to Solyndra so Vice President Joe Biden could announce the approval at a groundbreaking for the company's new factory in September 2009.
The Washington Post report was based on emails between the Office of Management and Budget and White House officials.
But White House spokesman Jay Carney said that the emails showed only that White House officials were seeking information on the loan to work out the vice president's schedule.
Republicans however charge that evidence shows that the White House, in its rush to push out stimulus spending, had cut short the final review process for the loan to Solyndra.
Critics of the administration say that the firm, once hailed as a shining example of Obama's push to create green jobs in a new energy economy, was instead an symbol of unwise federal handouts.
California-based Solyndra has now filed for bankruptcy, closed its doors and laid off 1,000 workers, leaving taxpayers on the hook for the US$535 million loan.
- AAP