The Udvar-Házy family came to the US in 1958, fleeing the Soviet occupation of Hungary. Hazy attended University High School in Los Angeles, and the University of California, Los Angeles.
Udvar-Házy was in his 20s during the later part of transition from propeller aircraft to jets during the mid to late 1960s, and realized that the higher capital investment required to purchase jet aircraft created an opportunity for a leasing Business. He founded ILFC with Leslie Gonda and his son Louis Gonda in 1973, leasing a single used Douglas DC-8 to Aeroméxico. He left ILFC in February 2010 to found Air Lease Corporation.
Udvar-Házy gave a US$66 million grant to the Smithsonian Institution that allowed the U.S. National Air and Space Museum to build the Steven F. Udvar-Hazy Center annex at Washington Dulles International Airport. The annex houses more than 120 aircraft and 140 space-exploration exhibits as of 2006, and also includes the Space Shuttle Discovery. Plans call for eventually installing over 300 aircraft.
The Udvar-Házy family contributed funds to build the Christine and Steven F. Udvar-Hazy Library and Learning Center at Embry–Riddle Aeronautical University's Prescott Campus. This donation is the largest to date made to the university. The Business building at Dixie State University is named after his parents.
In 2016, Prime Minister of Hungary, Viktor Orbán presented Udvar-Házy the Grand Cross of the Order of Merit of Hungary for his achievements in airline industry.