The EOC held a secret ballot at its 41st General Assembly in Rome with 38 voting in favour, eight against and three abstaining.
The event, which will take place every four years, will include 15 Olympic sports and two non-Olympic sports which are yet to be chosen.
"There are plenty of technical details to decide, but the Assembly has above all shown its will to go ahead, and make this sports event, which is in no way intended to be a copy of the Olympic Games, a tool with which to enhance the attractiveness of sport," the EOC wrote on its website.
"The NOCs (National Olympic Committees) have received assurance that the event will not cost them a penny, but bring them financial gains.
"Baku will be a test, that it is hoped will turn into a long series in years to come."
There has been considerable opposition to the idea of a new Games event, particularly from the European Athletics Association which has already voted against the participation of its members.
The EOC is also likely to have problems convincing other sports that already have well-established events in a packed European calendar, with swimming being one of the key Olympic sports that would struggle to find time for the new event.
Baku was the only city to offer itself as a candidate for the inaugural Games, which are likely to be held in May 2015.