Bing announced they added a feature named the Site Move Tool to Bing Webmaster Tools.
Yea, Google does have a "Change of Address" tool but this tool does a bit more than what Google's tool does. Bing was clear to mention that:
Whereas other Webmaster Tools only allow a "Change of Address" from one domain to another, we wanted to allow web publishers more flexibility.
It offers two things, one of which Google does not offer.
(1) Moving a ton of URLs from within the same domain. For example, you upgrade your CMS and all your URLs change but you are still on the same domain name. This tool allows you to communicate the mass URL change.
(2) A typical domain name to domain name change. For example, you finally acquire the domain name of your dreams and you migrate your site from the old domain name to the new one.
Just like the Google change of address, Bing still wants you to have your 301 redirects in place.
Bing also has two caveats; (1) you must set up the redirects to a new domain that resolves, and (2) once you do the move, you cannot issue another move request for six months.
Forum discussion at Google+.