Sign up to MailChimp and integrate it with your website through any number of widgets and plugins, I’d just go for one of the simple ones but I have had success with some of the automatic newsletter plugins too.
You can have your blog content automatically loaded into your MailChimp newsletter, and even sent out automatically on a schedule that you pre set. While this is no substitute for a hand-crafted newsletter with specifically selected and targeted content, it is a very useful way to keep consistency in your communication without having to do any more than post to your blog.