1. Create an account on the new server.
2. On the new server, go to Settings -> Account, and under “Moving from a different account” you’ll see a link to create an account alias. Put in your old account
3. On the old server, go to the same settings and create a redirect to your new account.

This will move all your followers to the new account, and anyone who goes to your old account will be redirected.

It will not move any existing posts, but those will live on at your old server.