The station said the broadcaster, who trained as a nurse and later a midwife, died peacefully in Southampton General Hospital on Wednesday evening with her husband and daughter present.
She recently told Chris Evans in a broadcast from her hospital bed that she had just weeks to live.
The broadcaster was one of the first female priests in the Church of England.
Station head Lewis Carnie said: "Reverend Ruth Scott was much loved amongst the Radio 2 family.
"Working with both Sir Terry Wogan and Chris Evans, her Pause For Thought reflections were enjoyed by millions of listeners to the Radio 2 Breakfast Show over the years.
"Our thoughts are with Ruth's family at this sad time."
Reverend Kate Bottley paid tribute on Pause For Thought on Zoe Ball's breakfast show, saying: "Christians - and vicars in particular - can often be accused of not living in the real world.
"That couldn't be said of Ruth Scott. She not only lived in the real world - she wanted to change it."
"Her congregations were lucky - Ruth wasn't your typical vicar - few can claim to have also trained as a magician and fire eater."
She added:: "Ruth's scripts were always honest. She was never one to dodge a harsh reality and in the last few years Ruth spoke movingly about her illness.
"During a spell when she felt well enough, Ruth and her husband Chris had few days break in Cornwall.
"They were out for a meal at a restaurant when the owner asked if they were celebrating anything in particular. 'Being alive,' Ruth said.
"The owner ripped up the bill. The meal was his gift. It was a generous present to a person who was generous with her time and her compassion. We have lost a radio friend."
Mrs Scott, who had been having cancer treatment for two years, told Evans: "I've got to accept the fact that I'm dying.
"I'm not frightened. I've had the most fantastic life. I just wish that it had been longer."
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