He said he was looking forward to working on a number of significant projects for the city, and for the Hawke's Bay region as a whole.
For the year ended 30 June, the report stated the total annual cost including fringe benefit tax to the council of Mr Jack's remuneration package was $318,730 - up from $288,719 in 2015.
Napier mayor Bill Dalton said in 2015 a review had been undertaken, after it was realised there had been "a historic underpayment of the chief executive of Napier City Council".
"We had a look at it and decided that the chief executive, who's doing a fantastic job for the city, we actually decided that he was in fact under-remunerated," Mr Dalton said.
In the past, there had been an informal way of attending to salary increases, so council had decided the appropriate way forward was to formalise this, Mr Dalton said.
Council hired Strategic Pay, "the foremost firm in New Zealand", to evaluate what council chief executives, and those in private enterprise, were being paid.
"It became very obvious that [Mr Jack] was significantly underpaid," he said.
A formal structure was developed so council could evaluate Mr Jack's contribution to the city, and now went through a formal procedure to evaluate his performance against a system of key performance indicators (Kips).
These Kips were around the requirements of his job, and what he was required to deliver to the ratepayers of Napier.
Mr Jack stepped into the role in September 2013, replacing Neil Taylor.
"There was a historic underpayment of the chief executive of Napier City Council because his predecessor would not accept salary increases, often in fact he turned them down time and time again," Mr Dalton said. "We ended up with a structure that underpaid our chief executive."
"We've got an extremely good chief executive and we want to ensure that we keep him," he said. "To keep him we've got to make sure that we offer him a competitive market rate . . . but he's still very much at the low end of the scale."