The 27-year-old, who suffered from two forms of leukaemia, passed away at his family home in Nottinghamshire, a press statement from Trinity Mirror said.
Adrian chronicled his battle against the disease on Baldy's Blog and later began a campaign for compulsory education about bone marrow donation in schools.
A blog post by Adrian's friend Liam at 9:51am this morning said Adrian died peacefully in his sleep.
"Every parent thinks their son or daughter is special and we are no different. Adrian touched all who knew him. We're very proud of all his achievements in tragically such a short time," said Keith Sudbury, Adrian's dad, in the blog post.
"Kay [Adrian's mum] and I hope that all Adrian's good work will be continued by all those who knew and loved him."
Adrian's blog, which attracted hundreds of commenters from across the globe, and campaign were picked up by national and international media, and lead to a meeting with Gordon Brown.
Last month Adrian handed a petition signed by 11,253 people to Ed Balls, secretary of state for children, schools and families, asking for a change in education policy to require educational institutions to teach students about bone marrow donation.
Adrian, who was named multimedia journalist of the year at Press Gazette's regional press awards, began his career as a journalist in 2003 as a junior reporter at the Express and Chronicle series in Holmfirth.
He joined the Examiner three years later and was promoted to digital journalist in charge of the paper's website in November 2006.
He became seriously ill only two days into his new job and weeks later was diagnosed with leukaemia.
"Adrian was a wonderful colleague and quite simply a brilliant journalist and we shall never forget him. His story has touched all of us at Trinity Mirror and won the hearts of the nation," said Sly Bailey, chief executive of Trinity Mirror, in a press statement.
"He showed tremendous strength and courage throughout his illness to raise awareness of bone marrow donation and always conducted himself with dignity and good humour. Our thoughts are with the family and friends of this hugely inspirational young man."
A private family funeral followed by a remembrance service is to be held at Sheffield Cathedral on a date to be confirmed.
An online book of remembrance has been set up as part of the Examiner's website.