The planned new venue will cost around £150m to build and the winning consortium is led by Live Nation.
The three-year build programme is expected to create over 2,000 jobs.
Cardiff Council Leader, Cllr Huw Thomas, said: “We remain committed to delivering a new indoor arena and today we have taken a big step forwards.
“I know there will be voices asking “how can the council afford to be involved in a project like this at this time”, that’s why it’s important they know that this is a private-sector led proposal which the council is supporting.
“That means the private sector will be covering the lion’s share of the costs and taking the vast majority of risk associated with delivering this project.
“The Council’s capital commitment will be less than 15% and could be significantly lower by the end of the process, and instead we will use the strength of our covenant to enable our partner to access funding at a more affordable rate.”
Cardiff Council’s Cabinet has now approved a report which authorises the preparation of the final detailed designs and costs before entering into a development contract in the summer.