Moments later, she announced that Sandra Kai Fong would be the deputy mayor of Rotorua.
Tapsell said Kai Fong was the highest-polling councillor.
Progress results for the election are yet to be officially released.
Tapsell, 30 is the first Māori woman elected to the role in Rotorua.
The final results will be announced late next week.
The last Māori mayor was Harry Dansey, in 1941.
Tapsell said she had a lot of work to do.
"We have a plan and we need to start moving forward."
"Rotorua, thank you so much, from the bottom of my heart... for now confirming that I am the best person to lead you forward... not only through the challenges but through all of the great opportunities that we have here in Rotorua.''
"I look forward to being that strong voice for you, I look forward to tackling those issues for you as soon as possible.
"We have such a great and such a bright future ahead of us.
"We did good, Rotorua."
Tapsell said she wanted to call all the successful councillors.
"It's very important that we have a functional council and work together so I'll be asking them what their top priorities are."
Progress results indicated Tapsell would be joined by councillors Sandra Kai Fong, Fisher Wang, Gregg Brown, Robert Lee, Don Paterson and Conan O'Brien on the general ward, Karen Barker on the rural ward and Lani Kereopa, Trevor Maxwell and Rawiri Waru on the Māori ward.
Outgoing Rotorua mayor Steve Chadwick told Local Democracy Reporting that Tapsell would have her work cut out for her with a "divided" council.
Chadwick said issues such as the council's reserves proposal and furore around Springfield's golf course were reflected in the results.
"It's going to need artful hands to manage it. There's quite clear division on this council."
She said the results were "very affirming" of the need for a Māori ward and she was "quite sad" Mercia Yates and Merepeka Raukawa-Tait appeared to have lost their seats.
Raukawa-Tait was at the top of unsuccessful candidates so finalised votes may change her result.
"[Yates] has been an outstanding and hard-working councillor."
Chadwick said big challenges such as housing and community safety would not "go away".
"The new council needs to work together and with the Government. We can't solve it on our own. I wish them all well."
Tapsell's mother, Roana Bennett, said her daughter was humble and committed, and would bring "intelligence and energy and the dedication the city needs".
She said people did not see how humble Tapsell was.
"She carries a lot of humility with her.
"Tania has always been interested and politics and grown up in a political family."
Her father Terry Tapsell was "absolutely elated. So happy for her. She just works so hard".
"Pretty fitting she was successful. We're just absolutely over the moon."
Rival mayoral candidate Fletcher Tabuteau confirmed he had received a phone call to say he had missed out.
"It has been a massive campaign. I am really proud of what I have done and I can't thank the people around me enough. I think it is important people put their hand up and be counted, and that is what I did."
Tabuteau, who was at home when he got the news, said he was soon to join his supporters at the Rotorua Novotel.
Tabuteau said he didn't consider standing for the council as he had a specific skillset and he wanted the top job. He said being on the council probably wouldn't have been enough for him.
Rival mayoral candidate Reynold Macpherson described missing out as "almost a relief", saying: "Given the problems Rotorua is facing, in some sense I have dodged a bullet".
Macpherson said Tapsell got more than 10,000 votes in the last election, so it was always going to be an "uphill battle".
Macpherson, who didn't stand for the council again, said the end of his time on the council wasn't the end of the Rotorua District Residents and Ratepayers' group.
"We have been campaigning for nine years and it's not going to stop. It is a very strong and very active interest group and we will keep going."
He said the group's annual general meeting is being held in November, and he was looking to step down.
"It's been nine years."
Unsuccessful mayoral candidate Raj Kumar said he was not "despondent" about the result as fellow ticket members Don Paterson and Conan O'Brien were elected.
He was looking forward to focusing on his family and business.
Kumar said if Tapsell could deliver what she had promised on the campaign trail, it would be a good thing.
"We just need to get behind her now and she what she can achieve."
Third-place mayoral candidate Ben Sandford could not be immediately contacted on Saturday afternoon, but Local Democracy Reporting understands he was playing cricket.
When council candidate Fisher Wang arrived at Tapsell's party, Tapsell yelled across the room with a very concerned look on her face, "Fisher. Are you in?"
"I want to thank all of the candidates who put their names forward. They can be proud of their campaigns. They raised important issues and were professional and respectful.''
Earlier, about 40 supporters steadily trickled into Tapsell's election party at Rotorua's Pullman Hotel. The group was mostly friends and family, including husband Kanin Clancy.
Tapsell, a three-term Rotorua Lakes councillor, announced her mayoral bid in May on a platform of stopping "the spend", building a safer community and "smart" investment.
Tapsell, who ran in the 2020 election as the National candidate for East Coast, is the great niece of Sir Peter Tapsell, a former Labour Party Speaker of the House and cabinet minister.
Tapsell was unsuccessful in her bid for the seat, losing to Labour's Kiritapu Allan by 6331 votes.
Progress results showed voter turnout in the district was 42.61 per cent, with 21,020 votes cast. Voting was down 2.6 per cent on the 2019 election, when 45.17 per cent of eligible voters. This year, there were 49,334 eligible voters in the district.
Tapsell is Rotorua's 15th mayor, and was first elected to the council in 2013 at age 21. At that time, she was the youngest elected councillor in New Zealand.
At her campaign launch, Tapsell said she wanted to increase the council's spend on crime prevention and community safety to $1.5 million annually, something she will need to get a majority of councillors to vote with her on.
She also said she would spearhead an operational review of the council and if necessary, a restructure aimed at delivering better value for money.
Tapsell wanted the council to invest in destination marketing and create a Rotorua development strategy aimed at enabling better housing and job opportunities.
During the term, Tapsell opposed the Rotorua reserves proposal and Three Waters reform.
Steve Chadwick, who has been the mayor since 2013, announced in 2021 she would not run again.