The opera singer's manager has warned that he risks damaging his eyesight with the treatment, which is aiming to eradicate a brain tumour that struck Watson down in 2007.
He told the Daily Star: "He's in as good as spirits as anybody can be with that kind of journey ahead.
"The doctors are very cautious - they want to get to it but because it's near the optic nerve, they've got to be careful not to damage the eyesight.
"It's a very arduous five-week period that the doctors hope will give him closure."
Speaking outside the hospital, Watson commented: "My throat feels ok. I feel a little bit tired.
"It takes a while to get your energy and stamina levels up again. It's been a strange new year, 2008, in for my radiotherapy on January 2."