Songbird was first released in 1998 and was picked up in the UK by Tony Bramwell, who runs Brighton label Hot Records.
Cassidy died of skin cancer in 1996 aged 33, a virtual unknown.
But her album Songbird, released posthumously, has been pushed to success by word of mouth and by the endorsement of BBC Radio 2, which included some of her songs on its playlist.
Hugh Cassidy, speaking to ITV's This Morning programme from Washington DC, said: "I'm thrilled to death at what's happening.
'Resonate'
"I had no idea she was going to blossom out into this. I mean, she just seemed to resonate with people - and something in her voice, which science hasn't discovered yet, resonated with people and grabbed them with the phrasing and dynamics."
Songbird was first released in 1998 and was picked up in the UK by Tony Bramwell, who runs Brighton label Hot Records.
He said: "Her voice is phenomenal. It's like a mixture of Aretha Franklin, Roberta Flack and the great soul singers."
He also introduced Paul Walters, producer of Terry Wogan's Radio 2 show, to her talent.
The song Over The Rainbow was then included on the presenter's playlist as a result.
Top 10
A cover of Sting's Fields Of Gold, made it into the top 10 of BBC Radio 2 listeners' all-time favourite tracks a couple of years ago.
The singer died four months after she was first diagnosed with cancer.
"We all had hopes of her recovering, but she passed away here in the home," her father said.
"We never for an instant thought this was it," he added.
She died before she had any inkling of the success she was to achieve. The album has now gone platinum in the UK.
Her father said she would have been unfazed by the attention.
"I know that if somebody mentioned it to her about her success she would give a big smile and lower her head, but I know she's thrilled inside," he said.