The 44-year-old actor replaces Matt Smith as Philip in the next series of the epic Netflix drama, which features Olivia Colman as the Queen.
An image of Menzies, in character, appearing to look out of a window at Buckingham Palace, was posted on Twitter with the caption “Ambition”.
Colman replaces Claire Foy in the title role and a previously-released image showed the now middle-aged Queen drinking tea.
The Crown returns in 2019, with Helena Bonham Carter taking over from Vanessa Kirby as Princess Margaret.
The first season portrayed the early days of the Queen’s reign, while the second series picked up in 1956 and continued through to 1963.