Dr Silvia Casale has been chosen to head the review of the Independent Police Complaints Commission (IPCC) probe.
It will consider whether police officers or staff should face misconduct or criminal charges over his death.
The IPCC’s original investigation found that police officers had acted properly, but was slammed by Mr Rigg’s family as “extremely poor and ineffective”.
Earlier this year the jury at the inquest into Mr Rigg’s death found that police officers used “unsuitable” force after arresting the 40-year-old schizophrenic for attacking passers-by and police officers in Balham, south London, on August 21 2008.
Physically fit Mr Rigg was being held at Brixton police station when he died of cardiac arrest.
Scotland Yard is currently carrying out its own review of how police deal with mentally ill people in custody.
Dr Casale will be assisted by legal adviser James Lewis QC, and Martin Corfe who is a forensic mental health nurse consultant.
She said: “The independent investigation of deaths in police custody is difficult and complex work. As one of the most important safeguards of the rule of law, it is vital for maintaining accountability and public confidence in the police.
“I hope that this review will contribute to the IPCC’s on-going efforts to ensure a fair, rigorous and thorough process of investigation as well as to the ultimate aim of preventing future tragedy, such as the death of Mr Rigg.”
She is due to report in the spring.
Dr Casale is a former president of the European and UN committees for the prevention of torture, and a trustee of the Prison Reform Trust.
The review is the first external probe into an IPCC investigation, campaign group Inquest said.
It sent a report by coroner Andrew Harris on Mr Rigg’s death to various Government departments yesterday.
In it he said: “Despite the passage of four years since Mr Rigg died, there is still a lack of clarity and incomplete understandings of the roles of different organisations and when they should communicate and act together – especially in an emergency.”