Lady Hale has been appointed as the first female president of the UK's highest court.
The news was announced in a statement from Downing Street on Friday.
Baroness Hale of Richmond, 72, who is currently deputy president of the Supreme Court, succeeds Lord Neuberger.
Yorkshire-born Lady Hale will be officially sworn in as president on October 2.
On the same date, the Supreme Court will welcome three new justices - including a second female judge, Lady Justice Black.
Lady Hale became the first woman justice of the Supreme Court in October 2009, and was appointed deputy president in June 2013.
After her appointment as president was confirmed, she said in a statement: "It is a great honour and a challenge to be appointed to succeed Lord Neuberger.
"I look forward to building upon his pioneering achievements, including developing closer links with each part of the United Kingdom, for example by sitting outside London, and improving the ways in which we communicate our work to the public.
"Recent high-profile cases mean that more people than ever before have heard of the Supreme Court, and we hope that this will help to create a broader understanding of how the judiciary serves society.
"While I, of course, look forward to working alongside all my colleagues, it is a particular pleasure for me to be taking up the post at the same time as we welcome only the second ever woman to sit on the UK's top appeal court."
Lord Neuberger said: "For Lady Hale to become president of the institution to which she has contributed so much is a fitting pinnacle to a truly ground-breaking career."
Statistics released on Thursday showed that the percentage of senior women judges had increased in the three years to April 2017 - from 18% to 24% in the Court of Appeal and from 18% to 22% in the High Court.