Sheila Campbell and her husband Frank adopted Nicky as a four-day-old baby.
The 58-year-old wrote on Twitter: “The day she and Dad adopted me was the day I won the lottery.
“I am so lucky and proud to have had her as my mum and we will miss her more than we can ever express. She was my adoptive mum. She was my real mum.”
Mrs Campbell, later a social worker, died on Wednesday, days after celebrating her birthday.
After missing presenting yesterday’s edition of his BBC breakfast show, Nicky said: “We made a BBC programme together about her service as a radar operator and she was immensely proud of her role on D-Day. Her life’s work was as a social worker helping others.”
Nicky, who has four daughters with wife Tina Ritchie, added: “She doted on her grandchildren and my girls completely adored her. Everybody did.”
Widowed Mrs Campbell revealed her role in the battle against the Nazis in an interview with her son, broadcast in June.
Stationed in East Sussex, she helped to guide RAF planes to their targets during the D-Day campaign.
Ahead of the 75th anniversary of the landings, she said: “I will be thinking of being up on Beachy Head, the radar and the landing craft below.
“I will be thinking a lot about the lives that were lost on those beaches at that time.”
Yesterday Nicky’s radio co-host Rachel Burden wept and was too upset to read Nicky’s message on air. It was then read by stand-in Geoff Lloyd.
Rachel said later: “Sheila Campbell was an incredible woman and I feel really, really privileged to have known her.”