The committee list was approved on the final day of the ruling Communist Party's five-yearly congress.
Zeng, 68, was a influential party leader long associated with Hu's predecessor, Jiang Zemin.
Luo Gan, a senior security official and Wu Guanzheng, an anti-corruption chief were also named as being off the list for the new committee, Xinhua said.
Jia Qinglin, 67, a long-time ally of Jiang, will remain on the committee.
The new committee will appoint a politburo of a few dozen members and a senior politburo standing committee, with an announcement on the new line-ups expected on Monday.
The membership of the politiburo and standing committee will signify how much power Hu holds, as well as who his potential successors and rivals are.
"Hu has the power; it's now up to him to decide how he wants to use it and what he wants to do," said Li Datong, a former editor at a party newspaper.
"But Hu won't be adventurous. That's not in his nature, and the party and country have already formed interest groups that any leader would find it very difficult to move."
Li Keqiang, party leader of the northeastern industrial province of Liaoning, is thought to be among the leading contenders for promotion.
The new inner core is also likely to include Xi Jinping, a party leader from Shanghai.