The journalist, who fronts the BBC News At Six, was first diagnosed with stage four bowel cancer in 2014, but is now facing a second fight.
Posting on Twitter, George told his followers it had be “tough dealing” with the news the disease had come back.
“Always knew cancer could come back but still tough dealing with disappointment,” he wrote. “Harder for my family.
“I know what I have to do: stay calm, stay content, stay fit and let doctors do their best.”
The BBC also said in a statement: “Everyone at the BBC sends George and his family their best wishes as he undergoes treatment and we will be thinking of them.”
The presenter was first diagnosed with the disease, which had spread to his liver and lymph nodes, in April 2014.
He endured two rounds of chemotherapy and several operations, including the removal of most of his liver.
He finished treatment in October 2015, and returned to work on BBC News just two weeks later.
However, in an interview shortly after, he admitted he was “under no illusions” his cancer could come back.
“I realised I wouldn’t give back a single day of the previous year’s experience,” he told The Telegraph. “I am a richer person for it.
“I get anxious and then there is a huge relief when the doctor tells me it is clear again. But I am under no illusions.
“The doctor warned me last year, ‘Your cancer knows the road, the pathway out of the gut’. It can happen again.”
Bowel Cancer UK has said the disease kills nearly 16,000 people every year in the UK. It is the second most common cause of cancer death in the UK, behind lung cancer.