About time it can take some depending on how you web site is crawled and how fast is the cache usually updated for your pages.
What is for sure is they will be in google's cache next time it will update it's cache, should be a mater of a week or so in most cases, but can end up being longer and won't necessarily will be made for all the web site at once or at the same rate.
Anyway, if you really think you've got a better domain name for your web site available it can be a great thing to migrate.
Migrating domain is easy to do but must be done with care. It would be a nice new topic for the SEO technique
forum I guess