Making long story short, here are steps to accomplish the transfer:
- Request the current registrar (in my case: Webio) to remove Privacy Protection and Theft Protection
- Request the current registrar (in my case: Webio) to give you authinfo code
- Start domain transfer at GoDaddy
- You should receive Transaction ID and Security code from the current registrar (requested by GoDaddy)
- Authorize transfer at GoDaddy using:
- Transaction ID
- Security Code
- Authinfo code
After that it should take around 7 days to perform the transfer. I received e-mail (from current registrar) that the transfer will be performed in a few days if I do not cancel it. It is some sort of theft protection. In your case (if you have different registrar) it may be different. E.g. you may need to confirm the transfer.
The best way is to contact you current registrar and destination registrar about the specific instructions. That’s what I did and both was very nice and helpful.
EDIT: Do not forget to change Nameservers and DNSes on GoDaddy after transfer is completed 😉