The 51-year-old singer posed for pictures and spoke to more than 100 fans who had queued outside HMV in Buchanan Street to meet her and collect copies of Standing Ovation: The Greatest Songs From The Stage.
Boyle came to fame when her Britain's Got Talent audition was broadcast in 2009. Her first album became the UK's biggest selling debut of all time.
Maureen McGeorge queued for an hour to meet the singer and was "very, very excited".
She said: "Not that I haven't seen Susan before, but I'm a big fan and it's always exciting to meet her. She's wonderful."
"When I went up to her she said 'There's a face I know'. She gets to know her fans. She's very good with them and gives it the personal touch.
"I just love her to bits.
"I got four copies of the new album, three for friends in America who are big fans and one for me, obviously."
The album contains a number of duets, and Ms McGeorge is particularly fond of Boyle's pairing with her idol.
"My favourites are the songs with Donny Osmond, because I think you can tell how much Susan enjoys it. She's said before he's her lifelong idol."
There was a mixed group of people queuing to meet the Scottish star and one fan thinks her background allows her to attract fans of all ages.
Greg Stevenson, 21, said: "I think it's her story, coming from nothing to a multi-million selling artist. That inspires people, and I think she is amazingly talented.
"She is a lovely lady and said she was overwhelmed by the number of fans who had queued to see her."