Koch and his medical team appeared at a news conference, The Wall Street Journal reported.
"We'll make this very brief because I've got to get a haircut and a shave," Koch said.
When asked how he was feeling, Koch, who was admitted to the hospital Dec. 4, said, "Terrific! Who wouldn't feel terrific going home?"
His doctor, Joseph Tenebaum, said Koch received treatment with antibiotics and antiviral medication.
The former mayor is "still recuperating," Tenebaum said.
Koch turns 88 Wednesday. He said a party planned for the occasion would not have been canceled if he had stayed in the hospital.
"I would have telephoned in," he said. "The party was going to go on whether I was alive or dead."
Notable deaths of 2014 [PHOTOS]