The man is now being urged to contact detectives, who said he may hold key information over the New Town sex attack.
Police said today they had a good response from the public and several witnesses had come forward.
A 21-year-old woman had been travelling home from a night out with friends in the city centre when a “smartly dressed” stranger pounced in Eyre Place at around 4am yesterday.
She was in a walled garden leading off the Canonmills street, behind a block of tenement flats, where she was sexually assaulted.
The passer-by stopped to help the woman after spotting her in a “distressed” state.
The street was taped off from the junction of Broughton Road to beside Smithie’s Pub in Eyre Place yesterday.
Detective Inspector Keith Fairbairn said there was an “inner cordon” around the garden area, which was being closely guarded by police.
Forensics experts were at the scene to gather evidence.
DI Fairbairn said: “She had been with friends and she was making her way from a night out in central Edinburgh.
“She does not know the man. The inquiry is in its early stages and we’re still working around various lines of inquiry.
“We’re very keen to trace a Good Samaritan that has come to the aid of the girl – he is believed to be a white Scottish male.
“We believe that between 3.30am and 4am he has come to her aid on Eyre Place. He will likely have information.”
The young woman, who is believed to have travelled to the Canonmills area from the city centre by taxi, did not require hospital treatment.
DI Fairbairn said he would appeal to anyone who may have seen anything in Eyre Place between 2am and 4am yesterday to come forward.
A dedicated police team has been reviewing CCTV footage in the area, and additional patrols have been put in place to reassure local residents.
DI Fairbairn said: “Police Scotland are committed to investigating these types of offences and we will have extra officers out.”
Members of the public living in neighbouring properties said they had been left shaken by the incident.
A woman who lives in the block of flats looking on to the garden, who asked not to be named, said: “I’m afraid. My boyfriend has lived here for eight or nine years.
“We had all the curtains closed this morning so we didn’t know what was going on until later. It’s worrying.”
Meanwhile, Chris Lee tweeted: “It happened in my garden, but police are telling me nothing. Bit unnerving.”
Police are looking to trace a man described as Asian, aged 20 to 30, with short dark hair, smartly dressed and possibly wearing a blazer.
He may have left the scene by travelling westwards along Eyre Place in a silver car.
Detectives are set to speak to the victim again to develop a more detailed description of the suspect.
In November last year, Police Scotland revealed a shocking 35 per cent increase in the number of rapes across the country, with 905 reported in the half-year from April to September 2013 against the same period in 2012.
But charity Rape Crisis Scotland warned the true figure could be much higher as its own data showed that only 17 per cent of women and children who had sought their help in the previous 12 months had also reported the attack to the police.
Anyone with information about the Eyre Place attack should contact Police Scotland on 101 or Crimestoppers on 0800 555 111.