When moving a WP site, why does wp-admin redirect to old site?

I am in the process of moving a WP site from one host to another. I copied the database and all the files, created a new database and imported the old one. I then changed the wp-config file. The home page shows fine, but when I try to access /wp-admin it takes me back to the old site.

The new site is a dev server where I plan to make style changes before I take the site live.

What am I missing about this transition? How do I get the site to respond to the dev url correctly?