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Mr Cadogan, along with the councillors, was sworn in during a swift first meeting in Alexandra yesterday.
He confirmed Neil Gillespie as deputy mayor, beginning his third term in the role.
Mr Cadogan said after the meeting he was excited about the council working together so the district could ''move forward''.
''I really thought there was enthusiasm in the group.
''It was great to see both the established relationship between the councillors and the welcome new councillors have received.''
During the meeting they received an annual report which showed $5.6million more revenue in the 2015-16 financial year than expected in the annual plan.
Cr Gillespie said it was a ''damn fine result''.
''There is a whole lot of work to be done and the processes will continue, but we're in a good space to be able to get it done.''
It was important to recognise former mayor Tony Lepper's contribution in getting the council into this position, he said.
There were two new faces on the council since last term, in Victoria Bonham and Lynley Claridge, who was previously on the council from 2001 to 2010.
They replace Clair Higginson and Steve Battrick, neither of who sought re-election.
Mr Cadogan also announced the chairmen and deputy chairmen for council committees.
Nigel McKinlay replaced Ms Higginson as chairman of the waste and property infrastructure committee, and Cr Bonham is the deputy chairwoman.