Khalid Jamal, 45, met the women via a dating website and took them to his house, where he invited them to look at his pet fish in his bedroom.
Jamal denied the charges and claimed the sexual contact he had with both women, in 2013 and 2016, was consensual, but a jury found him guilty. He was remanded in custody ahead of sentencing next month.
The High Court in Glasgow heard the first woman, now 27, had been out with Jamal on a number of occasions.
But on Christmas Eve 2013 she was attacked by him while he tried to persuade her to have sex. He only stopped when she convinced him she would come back to his flat on Great Western Road, Glasgow, the next day if he did.
The witness described the experience as “really scary” and said he drove her home in a car ride that was “really eerie, totally silent”.
She added: “I just felt lucky, I was lucky nothing worse happened.”
The jury heard that his second victim, then 19, was taken to his house – described as a “cabin” in Balloch, West Dunbartonshire – where he raped her, between April and May 2016.
Jamal told his second victim he was 24 and on their first date picked her up in Glasgow city centre. Back at his house, she initially had no concerns, but Jamal suggested they went to his bedroom, where there was room for them to both sit down.
Jurors heard he stripped off in front of her and after she moved away from him on his bed, he pushed her down and raped her.
She told how she shouted at him, and he told her: “It’s fine.”
The teenager screamed at him to get off, then “gave up trying to fight him” until the attack came to an end.
He then took her home and she later sent him a message saying she didn’t want to speak to him because he had hurt her.
The teenager saw him again months later in September, when Jamal – who has been suspended by the General Medical Council – promised to drive her home from a night out. Instead, after claiming he had “a shot of alcohol” and couldn’t take her home, he drove her to his Parkhead flat and attacked her.
Advocate depute Stewart Ronnie told the jury that with both girls there was some sort of conversation about “come and see his fish”.