The shuttles were awarded to museums in suburban Washington, Los Angeles, Cape Canaveral, Fla., and New York.
Two losing cities - Houston and Dayton - had asked for an investigation, alleging political influences.
In a report released Thursday, Inspector General Paul Martin found there were no outside influences, including none from the White House. The decision making was based on attendance, population, funding and the facility.
There was a scoring error for the Air Force Museum in Dayton and it should have tied the winning cities. But NASA chief Charles Bolden told investigators that the cities he selected fit NASA's science education goals better.