Well, rel=canonical will technically work fine, however in this case if you are migrating the entire site (presuming you have all pages on the old domain, going somewhere on the new domain, I would essentially setup 301 redirects from the old domain to the new domain.
I don't think you should do anything in the webmaster console. Just remove all the pages from the old domain and setup 301s from old domain to new domain. Google Webmaster Console Site migration IMO is for scenarios like you have yourdomain.net and you acquire the domain yourdomain.com and want to migrate the domain from .com to .net or if you change the brand name to yourbrandname.net or so on.
Does that make sense ? I hope that helps.