Cronin was released from jail in Northern Ireland earlier this month after serving his latest sentence for a catalogue of crimes stretching back over 25 years.
He has now returned to Tranent, and, although there are no restrictions on his movements, police have confirmed they are keeping a close eye on him.
A police source has said that it is only “ a matter of time” before he reoffends.
It is the first time that 41-year-old Cronin has lived in Scotland since being released from prison over 15 years ago for a horrific attack on a Tory party worker, known as Judy X, after conning his way into her Edinburgh home after posing as a priest.
Since then he has committed a string of more than 50 offences in England and Ireland, including dishonesty and fraud.
Experts have dubbed him as incurable and “one of the most dangerous sex offenders in Britain”.
Cronin was first jailed for sexually assaulting a 14-year-old girl.
But it was his attack on Judy X in 1992 that thrust him into the national headlines.
He sexually attacked and then savagely beat the Conservative party activist.
He was jailed for life but had his sentence cut to only six years on appeal.
He was not placed on the sex offenders’ register, as it had not been created at the time of his original offences.
He was released early from jail on June 1 after being sentenced to a year for stealing £50 from a group of nuns.
A Police Scotland spokesman said: “A 41-year-old man has been bailed to an address in Tranent.
“The decision to allow bail and the conditions imposed are a matter for the courts.
“Police Scotland works closely with partner agencies to ensure any individuals requiring supervision are monitored robustly and that local communities are protected at all times.”.