Ziebell, who was contracted for next season, has signed a five-year deal, tying him to the club until at least the end of the 2021 season, when he will be 31-years-old.
Wright has signed a three-year deal, keeping him at Arden Street until 2018.
Both were selected in the 2008 National Draft, Ziebell was pick No. 7 and Wright was pick No. 28.
They were also teammates at the Murray Bushrangers during their time in the TAC Cup.