I've made all of my http pages 301 redirect to their https equivalents.
I've also made sure that all of the URLs in my sitemap files are https.
Lastly I created a new profile in GWTs under the https version of the site, and submitted the sitemaps in there (and removed them from the http version of the site). I suspect this was unnecessary, but I don't think it'll have done any harm.
Is there anything else I need to do, or is it just a matter of time for google to re-crawl and update their index?
Thanks