Robertson was born on 2 June 1886 in Woolwich in south-east London, but at the age of one-and-a-half he emigrated with his parents to California, settling in the San Joaquin Valley.
His initial plan to study basic biology was changed by a meeting with an American medical student while on holiday in Germany.
After attending some lectures on anatomy, he decided to study medicine, being admitted to the University of California in 1906.
After World War I, he accepted an associate professorship at the Peking Union Medical College in Beijing, China.
In 1927 he returned to USA, and accepted a position as head of the Department of Medicine at the University of Chicago.