The stamps feature the main characters in the BBC series which ran from 1968-77, including Corporal Jones's "Don't Panic", and Captain Mainwaring's "Stupid Boy" in describing Private Pike.
Other characters on the stamps include Private Walker, Private Frazer and Private Godfrey.
Ian Lavender, the only surviving member of the group of actors who played the Home Guard in the series set in the Second World War, said it was "overwhelming" to be featured on a stamp.
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He said: "I didn't believe you could have someone still alive on a stamp apart from the Queen. Being on a stamp is not something you hope for simply because it is so unlikely.
"You can hope for an OBE or a Bafta - those are things that happen. But to be on a stamp, well it really is so nice. What a lovely surprise."
Philip Parker, of Royal Mail, said: "Few TV comedies have inspired as much affection, or given us as many catchphrases, as Dad's Army. On its 50th birthday we hope these new stamps will raise plenty of smiles."
Dad's Army was about a Home Guard platoon commanded by pompous bank manager, Captain Mainwaring, and assisted by his mild-mannered chief clerk, Sergeant Wilson, with a motley band of men providing Walmington-on-Sea's last line of defence against the seemingly imminent Nazi invasion.
In its 1970s heyday the show regularly attracted more than 18 million viewers, becoming one of the most watched television programmes of its time.
The stamps will be available from 7,000 post offices from June 26.