Kakkar was appointed to the post by British Prime Minister David Cameron. The appointment will be for a single non-renewable term of five years and will be effective from October 1.
"I am pleased to appoint Lord Kakkar to this role. The committee will benefit hugely from his vast experience and integrity. I am grateful for the contribution Lord Jay has made over the last five years," Cameron said in a statement.
In its position as an advisory non-departmental public body sponsored by the Cabinet Office, the commission selects independent members on merit and on their commitment to the work of the House of Lords, in scrutinising legislation, sitting on committees and participating in debates.
Lord Kakkar is Professor of Surgery at University College London (UCL) and Consultant Surgeon University College London Hospitals NHS Foundation Trust since 2011.
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His research interests focus on the prevention and treatment of venous and arterial thromboembolic disease and cancer associated thrombosis.
He is chair of the Health Honours Committee, a member of the General Medical Council (GMC) and a Commissioner of the Royal Hospital in Chelsea.
As the new chairman of the Lords' Appointments commission, he will be paid on the basis of a non-pensionable salary of 8,000 pounds per annum and expected to commit an average of two to three days a month.
The Political and Constitutional Reform Committee held a pre-appointment hearing on July 18 and published a report on the choice of Lord Kakkar for the post.