Baroness Hale is expected to become the first female president of the Supreme Court, it is reported.
She will be confirmed in the role later on Friday in an announcement from Downing Street, The Times said.
Baroness Hale of Richmond became the UK's first woman Lord of Appeal in Ordinary in January 2004, before the establishment of the Supreme Court in 2009, following five years sitting in the Court of Appeal and five years as a High Court judge.
She became the Supreme Court deputy president in 2013, and at the time described the appointment as an "honour and a privilege".
After graduating from Cambridge, she taught law at Manchester University from 1966 to 1984, also qualifying as a barrister and practising at the Manchester Bar.
She specialised in family and social welfare law, was founding editor of the Journal of Social Welfare and Family Law, and authored a pioneering case book on the family, law and society.
In 1984 she was the first woman to be appointed to the Law Commission.