Salomon, who was Jewish, was born in Schlesswig-Holstein on December 25, 1836. He was elected a Chicago alderman of Chicago's sixth ward in 1861, one of the youngest alderman in Chicago history. Salomon enlisted as a second lieutenant in Colonel Frederick Hecker 's 24th Illinois. Disagreements arose between Hecker and some of his officers, after which Hecker and his supporters resigned, including Salomon.

In August 1862, Hecker formed a new regiment, the 82nd Illinois or the 'Second Hecker Regiment', composed mainly of German, Jewish, Swedish and other European volunteers. Salomon had the rank of lieutenant colonel.

Salomon became a hero during the Battle of Gettysburg. He had two horses shot out from under him. Carl Schurz described him during the battle: "He was the only soldier at Gettysburg who did not dodge when Lee's guns thundered; he stood up, smoked his cigar and faced the cannon balls with the sang froid of a Saladin..."

Early in 1864 Hecker resigned leaving Colonel Salomon was in charge. Salomon led the regiment during the Atlanta Campaign and through the capture of Atlanta. Assigned to deliver messages to Nashville, he missed the famous march to the sea. In December 1864, he rejoined the regiment and finished out the war with them. He was brevetted a brigadier general.

After the war, he returned to Chicago where he was elected clerk of Cook County.

In 1869 President Ulysses S. Grant appointed Salomon governor of Washington Territory. He was caught up in the political scandals of the Grant administration and resigned in 1872. The Pacific Tribune on his resignation, lauded his honesty and integrity. General Philip Sheridan led a delegation that presented him with a silver table service in recognition of his fine record of service, high qualities as a citizen and as a friend.

He moved to San Francisco where he practiced law. In 1898 Salomon was appointed assistant district attorney for the city and county. He was elected to the California state assembly in 1888. Salomon died at the age of 76 in 1913.