Configure 301 redirects on the old mobile URLs to point to the responsive
versions (the new pages). These redirects need to be done on a per-URL basis,
individually from each mobile URLs to the responsive URLs.
Remove any mobile-URL specific configuration your site might have, such as
conditional redirects or a vary HTTP header.
As a good practice, setup
rel=canonical on the responsive URLs pointing to themselves
(self-referential canonicals).
If you're currently using dynamic serving and want to move to responsive design,
you don't need to add or change any redirects.
Some benefits for moving to responsive web design
Moving to a responsive site should make maintenance and reporting much easier
for you down the road. Aside from no longer needing to manage separate URLs for
all pages, it will also make it much easier to adopt practices and technologies
such as hreflang for internationalization, AMP for speed, structured data for
advanced search features and more.
As always, if you need more help you can ask a question in our webmaster forum.