Richman featured 53 times for Port Vale
Altrincham have signed midfielder Simon Richman from Worcester City and defender Chris Lynch from Hyde.
Richman, 21, began his career at Port Vale and 20-year-old Lynch started out in the youth set up at Burnley.
The club have also agreed new deals with Michael Twiss, Stuart Coburn, Robbie Lawton, Anthony Danylyk, Nicky Clee, Ryan Brown and Shaun Densmore.
And the Robins have offered fresh contracts to Damian Reeves, James Smith and Robbie Williams.
But Dale Johnson and Marc Joseph have declined new deals, and Altrincham have been unable to offer terms to Chris Denham, Mark Beesley and Craig Dootson.