The American Horror Story creator and new father shared a picture of Logan Phineas Miller Murphy with fans and friends.
The tweeted photograph of Murphy's new son was also accompanied with a short message.
"Thanks to everyone for the kind wishes," he wrote. "Logan is one week old and doing great. Happy new year!"
Murphy and his photographer husband David Miller welcomed their new son on Christmas Eve.
Logan was born at 9.47am, and weighed in at 6lb 6oz.
The Glee creator and his husband originally broke the news that they would be first time parents back in October 2012.