"I've spoken to him and he's obviously delighted and looking forward to it."
Carter would be back with his wife in New Zealand in mid-December, Mr Hegan said.
Honor Carter also tweeted her excitement: "Time to share our exciting news ... @DanCarter & I are expecting our first child! I am 21 weeks & we are both very excited :) #BabyCarter".
Former rugby league international Monty Betham was among those who passed on their congratulations on Twitter.
"2 highly motivated & successful people. Now you will have even more purpose in your lives. #Congrats. #TeamParents."
Carter and Honor, a former New Zealand Black Sticks hockey player, married last December.