Mr Donaldson said he was both honoured and humbled after accepting the invitation from Mrs Chadwick on Saturday night.
"I am immensely excited by the challenge ahead. I'll get stuck in and do the best job I can to support Steve who I've known for a very long time."
Current Deputy Mayor Trevor Maxwell, who had held the position for the last nine years under Kevin Winters and for two years under Grahame Hall, said Mr Donaldson was an excellent choice.
Mrs Chadwick told the Rotorua Daily Post Mr Maxwell would become the council's cultural ambassador, a role he was perfectly suited for.
"Steve has told me she has a better role for me on the council," Mr Maxwell said.
"I think Dave is a worthy person to be given the nod and I have a lot of time for him, he has been a very good councillor.
"I've thoroughly enjoyed my time as deputy, there is no bitterness about it from me.
"I'm obviously disappointed for Kevin, but now we all know what we are getting into and it will take a bit of the load off my shoulders as well.
"I'm keenly anticipating what will happen in my new role and working with our new mayor."