"Formula One will be held in Baku in autumn 2015," ministry spokeswoman Samaya Mammadova told The Associated Press, adding that "the final signing (of contracts) will be at the end of May."
Mammadova said the race will be held shortly after Baku hosts the inaugural European Games multi-sports event in June.
Baku has hosted sports-car racing on a street circuit every year since 2012.
She said the signing ceremony in Baku will see contracts exchanged between F1 bosses and Baku Grand Prix, a private company.
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Azerbaijan would be the second ex-Soviet country to hold an F1 race after the inaugural Russian Grand Prix this October in the Black Sea resort of Sochi, which hosted the Winter Olympics in February.
The 2014 F1 calendar contains 19 races, and additional events in New Jersey, Mexico and India have been proposed for next season. That would potentially break the record of 20 races in a season, set in 2012.
Azerbaijan has been keen to establish itself as a sporting power in recent years. The country submitted bids to host the 2016 and 2020 Summer Olympics but was eliminated on both occasions before the final vote.
Azerbaijan hosted the 2011 world amateur boxing championships in Baku in one of its largest sports events yet.
The European Games are an attempt to imitate the Pan-American Games and Asian Games as regional multi-sports event modelled on the Olympics. The competition will feature 19 sports and a total of around 6,000 competitors, organisers say.