You can use the Jetpack plugin for Wordpress to generate newsletters from blog posts for free.
It also allows you to capture emails in wordpress, and then automatically email people every time you publish new blog posts.
All you have to do is to install and activate the plugin and switch on “A_llow users to subscribe to your posts and comments and receive notifications via email_” at Jetpack > Settings > Discussion in your site’s Dashboard.
You should also consider adding it;s widget on your blog sidebar to enable you easily capture email leads. You can also add the email subscription anywhere on your WordPress site using it’s shortcode.
More info at :Subscriptions
Alternatively,
You can use Feedburner or premium email newsletter services like Mailchimp, Mailerlite etc