Hilary McClintock was elected as mayor of Derry City and Strabane District Council on Monday. The SDLP's Jim McKeever is the new deputy mayor.
In 2012, the DUP mayor of Londonderry Maurice Devenney refused to hand his chains to Sinn Féin's Kevin Campbell.
Mayor McClintock said it was "significant" but things had moved on.
"Its part of the process towards normality, the same thing happened in Belfast council a few days ago," she said.
"It was something that we discussed locally and it wasn't really a big deal so we're quite happy to accept it (mayoral chains) from the outgoing mayor."
The Drumahoe based councillor said that during her term she wants more investment because people in the north west feel like "second class citizens".
"I don't want us to be second class I want us to punch a bit higher and I will hopefully lead on that," she said.
"I don't think it's even a party thing. I think west of the Bann we sometimes do feel neglected.
"There's a lot more that can be done for the city, in terms of unemployment we have absolutely woeful figures.
"We do need to bring more jobs and more infrastructure," she added.
Family, friends and councillors from different parties clapped and cheered as former mayor Elisha McCallion placed the mayoral chain around Mrs McClintock's neck.
The former mayor told BBC Radio Foyle she was delighted to be able to do so.
"I'm delighted everything went well for the new mayor and I want to wish her all the best for the future, and the deputy mayor as well," Mrs McCallion said.
"Its a very symbolic day because that was actually the very first time a DUP mayor has accepted a chain from a Sinn Féin ex-mayor.
"It just goes to show you where we are as a society here in this city so I was delighted to do that honour," she said.
Mrs McClintock, who is married with two daughters, has previously worked as a civil servant and a classroom assistant.

WWT Washington Wetland Centre has sighted 16 adults and 21 young this year, in comparison to 23 adult birds last year.
They have nested by a lake and shingle island which expanded by the centre last autumn. Breeding at the site started in 2006.
Reserve manager John Gowland said it was a "real conservation success story".
"The high number of youngsters is a positive sign on the success of the improved shingle islands and emphasises the growing confidence of the nesting adults," he said.
The birds, which are a rare on Wearside, were once declared an extinct breeding species in the UK.
The avocet returned in the 1940s and is the emblem of the RSPB.
For the first time in Londonderry an outgoing Sinn Féin mayor has placed the chains of office around the neck of a DUP successor.
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A wildfowl centre has recorded its highest number of rare avocet birds.