Unfortunately there is no option for this on subdomain-level. So now what I did is registered my new custom domain as separate site and verified it. Now there are two site in my Webmaster Tools, my subdomain Tumblr URL (which is now a redirect, not even a page) and my custom URL.
Is there a negative affect for this, or should I just delete my subdomain site from Google Webmaster Tools and remove the verification tag?
There is no problem with redirection since Tumblr handles it really well, even my old pages are properly linked.
It is just weird to see that still I can see my Tumblr subdomain on popular searches, and no results for my new custom domain.