The futuristic 156,000 sq ft arena will be part of a wider leisure complex that is expected to cost around £50m to build.
The council will also advertise for a contractor to build the Arena this month with view to appointing a firm in the Spring, when it is hope work will begin.
As well as offering an indoor cycle track, the Arena has been designed to hold an audience of 5,000 which will allow Derby to stage cultural events, exhibitions and conferences.
Mace Project Director, David Grose, said: “We have designed an iconic building which will complement Pride Park Stadium, but will also function as a stand-alone facility.”
“The sculptured form will be very striking, exhibiting fluidity and movement to reflect the activities taking place inside”
Claire Davenport, director of leisure and culture said: “The multi-sport Arena will provide the city with fantastic modern facilities to be proud of and will form part of our lasting Olympic legacy for the people of Derby.
“Our commitment to transforming Derby’s leisure facilities will play a key role in the future economic growth of the city not to mention benefiting generations to come.”
The Arena will sit on the existing park and ride facility, so around 600 new spaces will be built between the Arena and football stadium to replace those lost and to provide additional capacity.