As long as you have your server / site configured to redirect the HTTP requests to HTTPS you should be good. This can actually HELP your SEO as google for example will push down sites without the SSL enabled.
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As long as the pages stay in the same location Google basically sees http:// and https:// as the same website. If done properly the transition can help with SEO. Here is more information on creating the redirects.
The redirects tell Google that it is the same page, and help visitors using old external links or bookmarks. It's best not to rely on the redirects for internal links, these should be updated with https:// if needed to avoid extra redirects.
Though it's not required, defining a canonical URL makes it clear to Google this is the best URL for a given page. (not a big deal to skip this as Google can figure it out based on the redirects and structure of the site)
It is also a good idea to use the free Google Webmaster Tools to make sure your website is being seen properly.