McKelvey was born in 1895 in Belfast, the son of a painter and decorator. He attended the Belfast School of Art and won the "Sir Charles Brett" prize for figure drawing there in 1912. By 1918 his work was exhibited at the Royal Hibernian Academy and in 1921 he was elected a member of the Belfast Art Society. McKelvey was appointed an associate of the RHA in 1923, being granted full membership in 1930. During his career McKelvey was considered on a par with Paul Henry and James Humbert Craig, two of the most successful Irish landscape painters of the time. He was elected as one of the first academicians of the Ulster Academy of Arts when it was founded in 1930. McKelvey died on June 30, 1974.