What should Yandex Webmaster and Google Webmaster do when changing the site domain?

Question

Search Engine Optimization

Hello!
There is a blog on Wordpress - 1.5 months.
About 100 posts.
I changed the domain, set a 301 redirect. The
question is what to do in Yandex Webmaster and Google Webmaster?
As I understand it, you need to delete the old site and add a new one.
And one more question - after what time can the old site be deleted altogether (after all, search engines must someday understand that the old site is no longer relevant).