Helmis was born in 1912 and started his football career at Ethnikos Piraeus in 1930. He stayed with Ethnikos until 1940. After World War II, Helmis joined Olympiakos, playing for the red-and-white club until the 1949 season.
During his career, Helmis was capped 6 times by the National Football Team of Greece. After his playing days were over, he coached Olympiakos between 1950 and 1954 and again in 1956, assisted by his brother, Vangelis. In between his two tenures, he coached the National Football Team of Greece.
Helmis died in 1981.