Yesterday Mr Jack - who was first appointed to the role in 2013 - said he was "absolutely thrilled".
He said he was glad to have the "opportunity to work with the elected members of council and the mayor, in the achievement of their vision for the development of Napier city".
"We've got some really exciting projects coming up that I want to deliver on, over the next couple of years."
These included the Napier Aquatic Centre redevelopment, and possible commercial development in the Napier CBD site currently occupied by the council's earthquake-prone civic buildings.
He was also looking forward to the expansion of the National Aquarium of New Zealand.
"That's hugely exciting for Napier and Hawke's Bay to create a facility that could be world class, but [also] to bring people to Napier and to get them engaged, and to change their behaviours around how we interact with our marine environment and what we do on land."
His other focus was on sustainability, namely work around Napier's storm water management and its drinking water network which is being chlorinated after E.Coli transgressions this year.
He has been reappointed for a five year term.
Mr Dalton said he was looking forward to continuing their working relationship over the coming years.
"He is a visionary. Together with myself, the councillors and staff, a great deal has been achieved for the city. Napier has never been so progressive and so well equipped to handle the growth that is already evident in our region.
"Mr Jack is unafraid of change, is a bold leader and has a depth of local government knowledge that is difficult to match. He is undoubtedly the right man for the job."
During his first term Mr Jack came under fire - particularly on social media - for controversial council projects and unpopular council decisions.
The criticism was such that Mr Dalton asked councillors to support the chief executive in the face of online "abuse".
However this led to scrutiny over the recruitment process, with allegations Mr Dalton was showing predetermination.
Mr Dalton has maintained the appointment of the new CE was a matter for council to decide - with the decision to reappoint Mr Jack for a five year term put to council during a public excluded portion of yesterday's meeting.
Mr Dalton said this was "standard practice".
"As with any recruitment process, deliberations are sensitive and do not take place in public."