Export Customer Data to MailChimp.
Cut down on your data entry woes and keep your automated email campaigns up-to-date. As New customers Comes this integration will automatically export their info to your MailChimp subscriber list.
Go to Integrations >> Mailchimp
Here, You have to export data with mail chimp as showing in attached screenshot. Also, Login to your Mailchimp account via http://mailchimp.com Enter Mailchimp API key and Mailchimp listed ID
Click on Save
Also, here is the video tutorial for your reference