Forrest H. Anderson was born in Helena, Montana, on January 20, 1913, the son of Oscar Anderson, a Swedish immigrant, and his wife Mary O'Keefe, an Irish immigrant. He attended public schools in Helena, and then studied pre-law at the University of Montana in Missoula. He got his law degree from Columbus University in Washington, D.C.

Anderson was admitted to practice before the Montana Supreme Court in 1938. He was elected to the Montana legislature in 1942, and also served as Lewis and Clark County Attorney. He was elected to the Montana Supreme Court in 1952 and served 4 years, before running for Montana Attorney General in 1956. He was re-elected as Attorney General three times. During the 1959 State Prison riot, he personally negotiated with the prisoners in helping to resolve the conflict. In 1968 he defeated incumbent Governor Tim Babcock, largely on an anti-sales tax platform. His slogan was "Pay More, What For?"

Anderson's one term as Governor was filled with controversy, but made significant accomplishments. The early years of his administration were dominated by conflict with Frank Dunkle, Fish and Game Commissioner, and the Fish and Game Commission, over the direction of the Commission on environmental issues and on fisherman and hunter access issues. In 1971 the Legislature deadlocked over a sales tax. Anderson called two special sessions to deal with the issue, and finally resorted to putting the tax to a public referendum. The sales tax was resoundingly defeated. Anderson actively supported the Montana Constitutional Convention. He later viewed his greatest Gubernatorial accomplishments as the Executive Reorganization, which combined several hundred agencies, boards, commissions, and councils, into 19 Departments; and his establishment of the Board of Investments to remove state funds from low yield bank accounts to place them in higher yield investment accounts. Anderson did not run for re-election due to health problems.

Anderson was also active in many civic and fraternal organizations. He married Evelyn Samson in 1941. They had three children. Forrest Anderson died in Helena on July 20, 1989, of a self-inflicted gunshot wound.