Hi Abhinav,
As per my research, I found that basically once you become a partner, you need to run a security scan on your code, make it a managed package, upload a copy to the AppExchange, create and configure a publisher profile and a listing, click on the “Start Security Review” on the listing, and fill out the required information. Security reviews are generally 5-7 weeks waiting time, and there is no charge for free apps. The rest of the process besides the manual review should only take an hour or two of time.
Thanks