Stephen Dickson had previously abducted two teenagers and tried to abduct another.
Judge Lord Doherty told Dickson: "In each case you preyed on the vulnerable. Your behaviour is extremely concerning and escalated until you finally abducted and raped your last victim."
He added: "I am in no doubt you pose a very serious danger to young women to the safety of their lives."
Dickson, 50, had been convicted of two assault and abduction charges, an attempted abduction, and the abduction and rape of the 15-year-old in Aberdeen.
At the High Court in Edinburgh Dickson was given an Order for Lifelong Restriction, under which the judge sets a minimum jail term but the offender is only released with Parole Board permission.
Lord Doherty ordered that Dickson should serve five years in jail before he becomes eligible to seek release.
The judge told him that was "the bare minimum period which you must serve".
He added: "When you are actually released after the expiry of that period will be a matter for the Parole Board to determine."
Dickson's counsel Donald Findlay QC had argued against the imposition of the order, saying it was a "draconian" measure.
Mr Findlay said the case "falls a long way short" of the type where a man could be deprived of his liberty for the rest of his life "subject to the view of the State".
Dickson had no history of crime, bar trivial motoring offences. "He is a family man," said Mr Findlay. "He has let them down very badly. He knows that."
Dickson targeted his first victim, aged 17, in October 2007 in the Wellington Road area of Aberdeen.
He approached her in the street, persuaded her to get into a car, and took her to another area of the city where he struggled with her and tried to handcuff her.
In December 2009 at Pittodrie Lane he attacked and tried to abduct a woman aged 18. He grabbed her by the hair and threatened violence.
Dickson, described as a prisoner, then attacked a 14-year-old in the city around New Year last year. He had again persuaded her to get into a car and driven her off before struggling with her and robbing her of a mobile phone, a camera and cash.
The rape victim was attacked on January 2 this year as she walked home from a friend's house.
Dickson pulled up next to her in Abbey Place. She said: "He grabbed my shoulders and chucked me in the back of the car."
Her arms were handcuffed behind her back and she was driven to Torry Battery where she was raped.
After Dickson was sentenced, her mother said: "On January 2 my beautiful daughter's life, my life and the lives of our family changed at the hands of this sexual predator."
During his earlier trial Dickson was branded "an insomniac prowler". Mr Findlay said Dickson did not accept he had committed rape.
The defence counsel said: "He seems to have developed some kind of notion that he could go up to comparative strangers, not just females, and offer them lifts."
Lord Doherty placed Dickson on the sex offenders' register for life.