Former Wycombe defender Hunt, 27, has agreed a one-year deal after impressing during the Bantams' tour of Essex.
Manager Peter Taylor told BBC Radio Leeds: "I'm very pleased to bring them in and they give us good competition and cover in key positions."
Moult, who has played twice for the Potters' first team in the Carling Cup, will join the likes of James Hanson, Gareth Evans and fellow new signing Jake Speight in fighting for a starting spot upfront.
I had Lewis Hunt at Wycombe and he is a very experienced defender. He has three promotions in his career too.
Peter Taylor
Taylor explained: "Louis is a clever striker and I'm very pleased with this signing.
"Even though he is young he is very intelligent and I'm hopeful he will come to us and do very well and score some goals.
"I think there were a few League One clubs in for him, so for a young age that shows what ability he has.
"He's trained with us today and once he gets to know everyone I'm sure he will be great for us."
Hunt, a former Southend player, can play as both a right-back and centre-back and earned his contract after a successful trial period at Valley Parade.
His deal could be extended, depending on the number of matches he plays for the League Two club.
"I had Lewis at Wycombe and he is a very experienced defender. He has three promotions in his career too.
"I was always very nervous that if Simon Ramsden got an injury then we wouldn't have any real cover in that position with a recognised right-back.
"Zesh Rehman can play at right-back, but he would say he is a centre-back not a right-back and I would agree with that.
"I'm very pleased with him, he fits the bill well, will handle being here well and brings good experience."
Source: BBC Sport
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