Met commissioner Sir Bernard Hogan-Howe has asked Sir Richard Henriques to make recommendations about whether there are ways to improve procedures.
The Operation Midland inquiry into a 1970s and 1980s paedophile ring is among inquiries that will be examined.
The force has come under fire amid claims it over-reacted to allegations.
Former head of the Army Lord Bramall, 92, who last month found out he would not face any further action in connection with Operation Midland, had called for a review.
His solicitor Drew Pettifer said Lord Bramall welcomed any review that would make "the process fairer and less painful".
The peer strongly denied claims made by a man given the name "Nick", and said detectives had taken 10 months before speaking to witnesses who cast doubt on the case.
There has also been scrutiny of the Met Police's handling of an investigation into a rape allegation against the late Lord Brittan, a former Home Secretary. He died in January 2015 without being told that the case had been dropped.
Critics have questioned whether Sir Bernard's contract, up in September this year, should be renewed.
Home Affairs Select Committee chairman Keith Vaz has asked that he appear in front of MPs to answer questions about the Met's handling of the cases.
Analysis: Press turns both barrels on the Met Police
Sir Peter Fahy, a former chief constable of Greater Manchester Police, told BBC Newsnight he felt some of the criticism Sir Bernard was receiving was unfair and that he was a "remarkable police leader".
However, he said that in the same position he would apologise to Lord Britten's wife for the delay in informing him his case had been dropped.
"There is clearly a particular issue about a delay... that is a clear mistake, an error. It is not how the procedure should work," he said.
"But I certainly think that no chief constable would apologise for investigating anybody."
Former Conservative children's minister Tim Loughton said allegations needed investigating quickly and a decision made quickly so people were "not left in the public domain hung out to dry and not given natural justice".
The judge's review will contain confidential and sensitive information and will be a private report for Sir Bernard, but its key findings and the recommendations will be made public later this year.
It will look at police procedure rather than evidence.
Sir Bernard said: "We are not afraid to learn how we can do these things better.
"Sir Richard brings an independent legal mind to advise us whether we can provide a better balance between our duty to investigate and the interests of suspects, complainants and victims."
He said Judge Lowell Goddard, who is chairing the wide-ranging independent inquiry into child sex abuse, had been notified of the review.
The announcement of the Henriques review is a significant moment.  The Met Police commissioner Sir Bernard Hogan-Howe is asking the judge: "Did we get it right or did we get it wrong?" when responding to allegations of child sexual abuse.
The idea is that this review will be able to answer the question fully and fairly because it will have access to confidential information not available to the Met's critics, especially those in the press.
Sir Richard Henriques has already decided police investigating Lord Janner in Leicester didn't do enough - now he will have to decide if the Met went too far, especially its most sensitive investigation, Operation Midland.
The fact that Sir Bernard has not waited until Operation Midland is complete to order this review, will be seen as a sign that it has failed.  He will be hoping for a more positive verdict.
Operation Midland, established in November 2014, is examining claims that boys were abused by a group of powerful men from politics, the military and law enforcement agencies at locations across southern England and in London in the 1970s and 1980s.
It is also examining claims that three boys were murdered. Operation Midland has focused on the Dolphin Square estate in Pimlico, south-west London.
Sir Richard recently carried out a review of sex abuse allegations against the former Labour MP Lord Janner, which concluded prosecutors had been wrong not to have charged the late peer 25 years ago.
Lord Janner's family have denied the allegations.
A spokesman for children's charity the NSPCC said it was crucial the review into the Met Police investigations did not "inadvertently discourage" victims of abuse from coming forward.
Gabrielle Shaw, from the National Association for People Abused in Childhood (Napac), said if the police could learn from past mistakes and get better at their job, that could only benefit society.
A former High Court judge is to review the Metropolitan Police's handling of cases involving claims of historical child abuse by public figures.