The agreement with the oil- and gas-rich country until the 2030 season applies to World Championship competitions in disciplines like freestyle, skicross, and snowboardcross.
"In addition to marketing rights, the core of the strategic partnership is to promote and develop Azerbaijan's status as a world-class winter sports destination", writes FIS in a statement.
The value of the sponsorship agreement has not been specified.
Azerbaijan has previously used revenue from oil and gas for sponsorship agreements with the European Football Association (Uefa) and the Spanish Atletico Madrid, and the country has also hosted Formula 1 races.
Azerbaijan wanted to host the 2016 and 2020 Olympic Games but has so far been rejected by the International Olympic Committee (IOC).