"After a long illness, Philip passed away peacefully this morning. We all send our sincere condolences to his family," the group said in a statement.
Chevron was a guitarist also known for his work with the band Radiators from Space.
He announced in 2007 he had been diagnosed with the disease. He underwent treatment and was declared cancer-free in April 2012. However, by August the same year doctors found a brain tumor that proved inoperable and ultimately fatal.