"I'm proud to have helped save this historical club and to have contributed in paving the way to its future success," the 59-year-old Italian told QPR's website.
Flamboyant former Renault team boss Briatore has spent almost 2-1/2 years at the club, having joined forces with Formula One supremo Ecclestone and steel tycoon Lakshmi Mittal to take it over in 2007 and help bring financial stability.
"Although my commitment to the club remains unchanged, I now feel the need to focus my energies into other fields," added Briatore, who will remain a QPR shareholder.
Ishan Saksena, previously the west London club's managing director, is taking over as chairman of QPR Holdings Limited while former club chairman Gianni Paladini, who became sporting director when Briatore arrived, will resume his former duties.
Mittal's family has taken the opportunity to increase its shareholding in the club.
