She was taken into a room strewn with rubbish, forced onto a mattress on a makeshift bed and raped.
Strachan warned her not to tell anyone about the attack or he would find her and hurt her.
He was caught days later after being spotted on a street by police officers.
Strachan, a former athlete with Edinburgh Athletic Club, also admitted repeatedly stabbing a man on the hand with a knife, causing severe injury, hours before the rape.
And he further pled guilty to attacking another man on the head with a claw hammer to the danger of his life on 28 May.
He was brought to the High Court for sentencing on 13 January this year, but fled the GEOAmey escort while being moved to a waiting vehicle.
Strachan admitted attempting to defeat the ends of justice by breaking free from his handcuffs and running off into the Royal Mile which sparked a mass manhunt.
He was detained by police a short time later.
Faye Cook, procurator fiscal for High Court sexual offences, said Strachan’s actions were “calculated, predatory, and caused profound harm”.
She added: “Although this type of stranger offending is rare, this conviction reflects the gravity of his crimes and the commitment of prosecutors and police to bring him to justice.”