Zaha Hadid is the first woman to win the top prize in the competition, now in its seventh year.
The overall winner was chosen by a panel of experts from more than 70 nominated designs in the categories of architecture, digital, fashion, furniture, graphics, product and transport. The judges also chose winners in the other six categories.
Hadid's Heydar Aliyev centre is the first architectural design to win the award.
Hadid said: "We're absolutely delighted to receive the Design of the Year Award.
"The surface of the Heydar Aliyev Centre's external plaza rises and folds to define a sequence of public event spaces within; welcoming, embracing and directing visitors throughout the building.
"It's an architectural landscape where concepts of seamless spatial flow are made real - creating a whole new kind of civic space for the city."
Heydar Aliyev centre located in Azerbaijan capital Baku houses a conference hall, a gallery hall and a museum.