Ninety six are believed to be living abroad while the rest are wanted for breaching notification requirements.
Conservative London Assembly member Tony Arbour said Londoners would be alarmed that 159 criminals "such as rapists and paedophiles" were lost.
The Met Police says the number varies because the information is dynamic and will change as arrests are made.
Under the Multi-Agency Public Protection Arrangements (Mappa), the national probation service, HM Prison Service and the Met are responsible for managing serious sexual and violent criminals once they complete their sentence.
The figures were released to Mr Arbour by the Met under the Freedom of Information Act.
In the response, the force said it believed 96 of the offenders were living abroad, with many having returned to their "home" country.
Mr Arbour said: "Londoners will be alarmed that the authorities are losing serious criminals such as rapists and paedophiles who may commit further crimes.
"If some of the 'wanted' offenders have left the country, as the police say, what is to stop them from re-entering our borders?"
Yvonne Traynor from the charity Rape Crisis South London said the figures were appalling.
"Something needs to be done to bring these agencies together to make sure that perpetrators are brought to justice.
"It takes a lot of courage for a survivor to report this serious crime to the police.
"The least we should expect is that proper procedures, by all agencies, are in place to ensure that perpetrators are held accountable and that other women and girls are safe."
In February 2012 the Met said it had lost track of 123 sex offenders.
Some 160 sex offenders being managed by authorities in London are missing, figures released show.