John Ellis Martineau was born in Clay County, Missouri. Martineau graduated from the University of Arkansas in 1896. He obtained his law degree in 1899 at the University of Arkansas. After graduation he served as a school administrator.
From 1902 to 1905 he served as a member of the Arkansas House of Representatives. He was appointed chancellor of the First Chancery Court in 1907 and served in that capacity until 1927.
Martineau was elected Governor of Arkansas in the 1926 election. The Martineau administration established a Confederate pensions board and authorized state aid to cities for highway construction through the Martineau Road Plan. In 1927 Martineau was forced to deal with a major crisis when the Mississippi River broke free of its banks and covered 13% of the state during the Great Mississippi Flood of 1927. Martineau was named president of the Tri-State Flood Commission. In May of 1927 Martineau called out the National Guard in response to the lynching of an African-American prisoner by a mob of 2,000 to 5,000 people in Little Rock. The crime gained national notoriety.
Martineau resigned from office on 2 March 1928 to accept an appointment to the Federal District Court of Eastern Arkansas, where he served until his death.
Martineau is buried at the Roselawn Memorial Park Cemetery in Little Rock, Arkansas.