Born in San Jose, California, Welsh read law to enter the bar in 1912. He was in private practice from 1912 to 1932, also serving as a deputy district attorney and a Superior Court judge of Sacramento County, California in 1914. He was a United States Commissioner for the United States District Court for the Northern District of California from 1914 to 1919. He served as a councilman on the Sacramento City Council from 1928 to 1929, and was Mayor of Sacramento in 1929. He was a member of the Board of Education of Sacramento in 1931, and served as a Judge of the Superior Court of California County of Sacramento from 1932 to 1939.^[1]

On June 21, 1939, Welsh was nominated by President Franklin D. Roosevelt to a new seat on the United States District Court for the Northern District of California created by 52 Stat. 584. He was confirmed by the United States Senate on July 11, 1939, and received his commission on July 14, 1939. He assumed senior status due to a certified disability on January 1, 1947, serving in that capacity until his death on January 4, 1953.^[1]

• Martin Ignatius Welsh at the Biographical Directory of Federal Judges, a publication of the Federal Judicial Center.