Ardern paid tribute to retiring Chief Justice Dame Sian Elias.
She said Elias had performed her role with excellence and had "represented New Zealand superbly on the international stage".
Today's announcement is significant because it is the first ever appointment of the head of New Zealand's final appellate court.
Under the Senior Courts Act, the Governor-General appoints the Chief Justice on the recommendation of the Prime Minister.
While there is no statutory process for the appointment, Ardern laid out a process earlier this year that included a shortlist prepared by the Solicitor-General, after consultation with a range of law professionals.
Ardern considered the shortlist and consulted with ministerial colleagues.
After the Solicitor-General confirmed the candidates' willingness to be appointed, the Prime Minister made her recommendation to the Governor-General, after consulting with Elias.
Although the process involves no formal consultation with the Opposition, Ardern is likely to have talked to shadow Attorney General Chris Finlayson about the decision, who has said he was "really comfortable" with the process.
When Elias was appointed Chief Justice in 1999, the Privy Council was the apex of New Zealand's court structure.
She rose to the Supreme Court when it was formed in 2004.
She served as a law commissioner from 1986 to 1990, was one of the first two women appointed Queen's Counsel in 1988 (the other being Dame Lowell Goddard), and was a judge of the High Court in 1995.
Winkelmann graduated with a law degree from the University of Auckland and was admitted to the Bar in 1985, when she was also awarded the Auckland District Law Society Centenary Prize for Best Graduate.
She was a partner at Phillips Fox (now DLA Piper) from 1988 until she became a barrister sole in May 2001, specialising in insolvency and commercial litigation.
She was appointed a High Court Judge in July 2004 and appointed as Chief High Court Judge in February 2010.
She joined the Court of Appeal bench in June 2015.
She is a member of the Board of the Australasian Institute of Judicial Administration, is the Chief Justice's representative on the Council of Law Reporting, and is the Chair of the Institute of Judicial Studies.
"The consultation process highlighted the enormous esteem Justice Winkelmann is held in by the legal community," Ardern said. "There was a high degree of consensus from all quarters for her appointment.
"Her Honour is recognised by her peers and the profession for her superior intellect, her judicial instinct and experience, coupled with strong leadership, qualities that I am sure will make an outstanding Chief Justice," Ardern said.
National Party Leader Simon Bridges congratulated Winkelmann.
"Justice Winkelmann has had a distinguished career on the bench since 2004, following a lengthy career as a litigator specialising in insolvency and commercial litigation. She served as Chief High Court Judge between 2010 and 2015, when she was elevated to the Court of Appeal.
"New Zealanders can have confidence that Justice Winkelmann will continue the fine tradition of Chief Justices in New Zealand upholding the rule of law and ensuring due process."
Bridges also paid tribute to Elias.
"To preside over the judiciary for almost two decades is a remarkable achievement, and jurisprudence in New Zealand has developed significantly over her time as Chief Justice."
In August, Elias warned of "civic disorder" if New Zealand did not find a way of resolving the imbalance that Maori and Pasifika suffer from in our justice system.
"It's not something we can continue to live with," Dame Sian Elias said following a speech at Maxim Institute's Sir John Graham lecture in Auckland.
"We are at risk of criminalising a distinct population. If that person (who asked the question) is accurate, we have a recipe for civic disorder," Elias said after being questioned over reports that 50 per cent of Maori and Pasifika had criminal records.
She will leave with a healthy superannuation entitlement seeded with at least $3.3 million of public money.
That payout, likely worth millions more, comes from a super scheme that sees judges, including Elias, able to contribute up to 5 per cent of their salaries to a superannuation fund that is then topped up by $7.50 for each dollar they contribute.
