Watts was nearing the end of a six-week course of radiotherapy at a hospital near his home in Chelsea, west London, the BBC reported.
He was diagnosed with the disease in June and has since undergone four weeks of the radiotherapy treatment.
The band's spokesman said: "He is expecting to make a full recovery and start work with the rest of the band later in the year."
Watts, 63, is a former smoker, but has not smoked since the 1960s, when the band shot to international fame.
His bandmates have been informed and he has been supported by wife Shirley during his radiotherapy.
Watts is said to be in "good form" and has been walking to the hospital for his treatment.
The spokesman said the band was currently taking a break from recording and touring.