Google Webmaster Tools now allows site owners to notify Google if you’ve changed domains. This “change of address” tool will update the search index for 180 days by which point your new domain should have been crawled and indexed.
The standard rules apply though, i.e. should still use a 301 permanent redirect for your old site to new domain. See Google’s own guidelines for moving an old to new domain.
3d rendering of sign via BigStock