Born in Okeechobee, Florida, Solomon served in the United States Marine Corps. Solomon was elected to the Warren County, New York legislature in 1968 and the New York State Assembly in 1972. Solomon was elected to the House of Representatives in 1978. Solomon supported the line-item veto, a constitutional amendment to ban flag burning, a repeal of the Assault Weapons Ban, and amendments which strengthed the Selective Service System. He was such an opponent of gun control that he once challenged Representative Patrick J. Kennedy of Rhode Island to "step outside" to settle a dispute over the issue. Solomon was referred to by his opponents as 'The Congressman from General Electric' (General Electric's headquarters were in Solomon's Congressional district). Solomon attempted to run for Speaker of the House in 1994 but withdrew in favor of Newt Gingrich. Solomon was the chairman of the House Rules Committee from 1995 to 1999, when he retired from Congress choosing not to be elected to an eleventh term.

Solomon was also the originator and sponsor of the Solomon Amendment, a controversial amendment to United States Code that precluded the receipt of federal government funds by colleges and universities unless they provided equal access to military recruiters as they did private employers. While superficially non-discriminatory, the policy was a direct response to the universal rule at American law schools to exclude employers who discriminated based on - among other categories - sexual orientation. The Amendment was subject to extensive litigation in 2003 by plaintiffs FAIR and SALT. See FAIR v. Rumsfeld, 390 F.3d 219 (3rd Cir. 2004). On March 6, 2006, the United States Supreme Court ruled in favor of the military and upheld the Solomon Amendment.