Note: This is a paid service according to WordPress.
1. Update your domain's name servers to the following. Make sure to remove any existing name servers that are already there. Once changes have been done, allow 4-24 hours (usually it takes 72 hours) for DNS propagation to take effect and then proceed to step 2.
NS1.WORDPRESS.COM
NS2.WORDPRESS.COM
NS3.WORDPRESS.COM
2. After the name server change takes effect, go to Upgrades -> Domains in your blog's dashboard, enter the domain into the form at the top of the page, and click the Add domain to blog button. If the name servers are verified, you will be prompted to pay for the upgrade and complete the process.
3. After the purchase is complete, go back to the Upgrades -> Domains page, select the radio button next to the domain you just mapped to your blog, and click the Update Primary Domain button.
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SOURCE: https://en.support.wordpress.com/domain-mapping/map-existing-domain
