The focus of the show's first episode was the Australian Labor Party's leadership battle between Rudd and Prime Minister Julia Gillard.
"We will be all over Kevin Rudd and we will be all over Julia Gillard, just like they are all over each other," Henry said.
Asked by Mr Rochford whether he is "Team Julia or Team Kevin," Henry replied: "If I had to be on that team, and I'm not, I would be Team Julia. Even though she has done such an appalling job managing Rudd."
Later on, Henry found the form he was known for on New Zealand television.
In a section called Henry's Hotline, one caller said she had never "seen two out of three more unprofessional newscasters ever in my life".
Henry quipped that she would become a "long-term Breakfast supporter".
Another asked, "Who's that bloke with the glasses on? I don't know him, I don't want him".
"That guy I actually didn't like," Henry responded.
One caller described Julia Gillard as a "disgrace to women in Australia". Henry said she sounded "like she's been drinking".
On Twitter, opinion was divided over Henry and his co-hosts' performance.
"This new @Channelten Breakfast show is pretty good. Paul Henry is a breath of fresh air," Stephen Cenatiempo said.
Mathan Allington agreed: "I like having Paul Henry on Breakfast TV in Oz. The other two shows were getting boring and predictable."
Peta Barclay also liked the new show.
"Paul Henry grilling (deputy opposition leader) Julie Bishop. Clearly this is what he was brought across the ditch for."
However, Henry had the same capacity to offend Australians as he did Kiwis on TVNZ's Breakfast show.
"Ten seconds of Paul Henry on Ten Breakfast and I've been offended already (by the comment) 'does the short man have feet on his bottom?'" Arion Ellis Potts wrote.
"Paul Henry makes me nauseous! NZ is such a beautiful country, if I lived there I'd send him away too!" Elizabeth Fletcher said.
Comments on the Channel Ten Breakfast Facebook page were mainly positive.
"Really enjoying the show! Great team and a refreshing change from the 'norm' ... love the dynamic," Georgina Jurevic wrote.
Jess Frost another was "loving the show. I usually watch Sunrise but I'll definitely be staying with you guys! Good work."
Henry resigned from TVNZ's Breakfast after admitting he had "crossed the line" after questioning whether Governor-General Sir Anand Satyanand was really a New Zealander.
He also mocked Delhi chief minister Sheila Dikshit's name.
Watch footage of Henry's first day on Breakfast here.
