The OED has this sense of Easter egg from 1987:
1987 Re: Does Set Startup work Anymore? in comp.sys.mac (Usenet newsgroup) 13 Nov., The Option-Command ‘About MultiFinder’ easter egg was a good laugh.
This and other early uses were hidden features in software. By 2009, it was being used for hidden clues in television shows:
2009 Wall St. Jrnl. 18 Sept. w7/5 Shows like ‘Damages’, ‘Lost’ and ‘24’ drop clues, or ‘Easter eggs’, as TV writers call them, into episodes that flash on screen for mere seconds.
I found an earlier example of the hidden software feature in Usenet, also in a Mac group.
25th April 1986, Re: a few more option-keys tips in net.micro.mac:
So many of these neat messages seem to come by, but I can't tack them
all up (very neatly) near the Mac. So here's a request to all you
hardcore MacFreaks out there (and I know you're out there!) -
have a periodically updated list of these option, command, and other
combination Easter egg type-of-things?
If you already have one, please, please post it to the net. If you
only have a few, please mail them to me at the address below, and when
it starts to get really huge, I post it back up again.
Wikipedia links to unverified anecdotal evidence of the term being used at Atari sometime after 1979. According to an interview with Warren Robinett, programmer of "Adventure" for the Atari 2600 which contained an early Easter egg:
What actually happened was that by the time some kid or kids had discovered the secret room and Atari found out, I didn't work there any more. So they couldn't really punish me, and the manager of game software at that time decided little hidden surprises in games, which he called "Easter Eggs" were kind of cool. Also, it would have cost $10,000 to make a new mask for the ROM in the cartridge. So what happened was that Atari left the secret room in the game.