Justice Rohini, 58, who was a judge of the Andhra Pradesh High Court, succeeds N.V. Ramana, who was elevated to the Supreme Court in February.
Justice Badar Durrez Ahmed has been the acting chief justice since then.
Justice Ramana was also from the Andhra Pradesh High Court.
Lt. Governor Najeeb Jung administered the oath of office to Justice Rohini.
Justice Rohini will be the 10th woman judge of the 40 judges in the Delhi High Court and is expected to stay for a period of four years.
Born in 1955, Justice Rohini studied at the Osmania University in Hyderabad and then at the College of Law, Andhra University, Visakhapatnam.
She enrolled as an advocate in December 1980 and later became chairman of the Andhra Pradesh State Bar Council. She was appointed a government pleader in the high court in 1995. She was appointed additional judge in 2001 and made a permanent judge in 2002.