The race, which will take place in the capital city Baku, would be run under the European Grand Prix banner, which has previously been used for events at the Nurburgring, Jerez and several others. The new venue will be a Hermann Tilke-designed street circuit.
"I am delighted to officially announce that we have signed a contract to bring Formula 1 racing to Baku in 2016," said Azerbaijan's Minister of Youth and Sport, Azad Rahimov.
"Our location at the crossroads of eastern Europe and western Asia is a new frontier for Formula 1 racing.
"Azerbaijan is a modern European country that has established a reputation as a centre of sporting excellence.
"The deal to bring Formula 1 racing to Baku is a very significant new chapter in our ongoing success to attract the world's largest sporting events to our country."
A statement from Bernie Ecclestone confirmed the deal.
"We are very happy that Baku has joined the Formula 1 family," said the F1 supremo. "This will be a street race, which will pass through interesting and picturesque parts of Baku.
"The event will meet the current Formula 1 criteria."
The announcement comes just days after F1 confirmed it will return to Mexico in 2015.