The actor will play a character named Canton in the next run's opening two-parter, which is set in 1960s America.
In a recent Twitter post, he wrote: "Doctor Who was definitely a dream job for me. Matt [Smith] is my favourite Doctor."
Sheppard also admitted that he is keen to appear in another of Who showrunner Steven Moffat's television projects.
"I really want [a role in] Sherlock," he added.
Sheppard's past television credits include roles in Supernatural, Warehouse 13, Chuck and Battlestar Galactica.
Doctor Who will return to BBC One later in the spring.