Justice Kaul was administered the oath of office by Haryana Governor Jagannath Pahadia at a ceremony held at Haryana Raj Bhavan.
Justice Kaul, 54, earlier served as the senior most judge of the Delhi High Court and was the acting Chief Justice there in September last year.
The strength of the Punjab and Haryana High Court Judges has gone up to 41 against the sanctioned strength of 68.
The post of the Chief Justice had fallen vacant on April 11 after former Chief Justice A K Sikri was elevated as a Supreme Court judge.
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Born on December 26, 1958, Justice Kaul was elevated as Additional Judge of Delhi High Court on May 3, 2001 and appointed as a permanent judge on May 2, 2003. Earlier, he was enrolled as an advocate on July 15, 1982.
Justice Kaul studied in the Modern School in New Delhi and then graduated in Economic (Honours) from St Stephen's College, University of Delhi in 1979.
Later speaking to reporters in an informal chat, Justice Kaul said one of his priorities would be to bring down the pendency of the cases.
There are 11.51 lakh cases pending in district courts of Punjab, Haryana and Chandigarh.
The effort would be to bring down the pending cases under 10 lakh over the next one year, he said.
With shortage of judges in the High Court also adding to the pendency of cases, Justice Kaul felt the ideal strength of the judges should be between 50-55 if it cannot go right up to the sanctioned strength.