A post on Bland's official Twitter account said: "Our beautiful, courageous Rachael died peacefully this morning surrounded by her close family. We are crushed but she would want me to thank everyone who took an interest in her story or sent messages of support. You'll never know how much they meant to her. Steve and Freddie xxx".
BBC Radio 5 Live tweeted: "Mother to Freddie. Wife to Steve. Our treasured colleague Rachael Bland has died. She inspired so many with her blogs, the chart-topping podcast #YouMeBigC and certainly put the can in cancer. We will miss her dearly."
Her family confirmed that she had died this morning shortly after 3am, the BBC said.
Her husband Steve told the BBC: "Rachael's death has left a huge hole in our perfect little family that we'll never be able to fill.
"She was an incredibly talented broadcaster as well as a wonderful and much-loved daughter, sister, aunt, niece, wife and, most importantly to her, a mother to her precious little Freddie.
"We all take such huge comfort and pride from the amazing and tireless work she has done since her diagnosis to reduce the stigma around cancer and prove that it is possible to live life to the fullest even when facing huge challenges on a daily basis. At the end, even though her body was at its weakest, her voice was at its strongest and most powerful.
"Rachael was and will always be an incredible inspiration to everyone she met. To us, she was perfect in every way and we will miss her more than words can say.
"We just ask that everyone respects our family's privacy as we try and come to terms with losing our beautiful girl."