Mayor Dave Cull started by saying Mr Orders' arrival at the council two years ago was like a ''breath of fresh air with a steel edge''.
Mr Orders had achieved an enormous amount in a short time and, more importantly, had gained the confidence, respect and affection of elected members, council staff and the community while doing it, Mr Cull said.
''You gave your all professionally, and socially, and we'll miss your advice, banter, wisdom and work ethic. You leave with this council's lasting gratitude.''
All returning councillors from the last term, except Lee Vandervis, stood to say a few words.
The council had had high expectations of Mr Orders, deputy mayor Chris Staynes said, and had not been disappointed with a man who had the ability to see very clearly what needed to be done, and did it by understanding and listening.
''I rank you among some of the very best leaders I have met in my career.''
Jinty MacTavish said she had personally learnt a lot from Mr Orders.
''I did not expect someone from so far away to pour so much of himself into the job.''
Andrew Noone, Kate Wilson and John Bezett also paid tribute, with Cr Bezett saying he believed Mr Orders' leadership was ''better than any other chief executive over the years I have been associated with the council''.
Richard Thomson said Mr Orders' easy manner with people and his management style had impressed him the most, with his willingness to do the tough jobs himself.
''We wish you all the best. I know you will enjoy a great challenge [at Cardiff Council, where Mr Orders is to take up the position of chief executive], just as you have enjoyed a great challenge here.''
New councillors Andrew Whiley, Neville Peat, Hilary Calvert and Mike Lord also wished Mr Orders well.
Mr Orders said he was humbled by the kind words. He and his family had enjoyed every minute of their time in Dunedin, and it had been a rewarding experience for him on a professional level.
To a ''significant degree'' that reflected the relationship he had with his management staff.
''We've had to deal with some tricky situations. Defusing landmines has become something of an in-house specialty in the DCC.''
He thanked the rest of the council staff, too.
''In my view, council is well served by the people who deliver its services day in and day out.''
And incoming chief executive Sue Bidrose would bring a perspective that would strengthen the council's ability to make the decisions it would have to over the coming years, he said.
