The former "Glee" star, 29, went public with her blossoming romance last month, when she was spotted on a dinner date with Robert in Santa Monica, California.
Michele and the "One Tree Hill" hunk are preparing to play out their relationship onscreen after signing up to feature in "Dimension 404", a six-episode anthology drama on streaming service Hulu.
She will portray Amanda, a woman who turns to online dating to help her get over a bad break-up, while Robert will play her suitor, Adam, who confesses his love for Amanda a little too soon.