Boschwitz was born in Berlin, Germany, November 7, 1930. In 1933 his family fled Nazi Germany. They settled in New Rochelle, New York, where he grew up. A graduate of The Pennington School, he attended Johns Hopkins University, Baltimore, Maryland and he graduated from New York University in 1950, and New York University Law School in 1953. He was admitted to the New York bar in 1954 and the Wisconsin bar in 1959. He served in the United States Army Signal Corps 1954-1955. He was the founder and chairman of a plywood and Home Improvement retailer, Plywood Minnesota which later became Home Valu Interiors.

Boschwitz was elected as an Independent-Republican to the United States Senate in November 1978 and was subsequently appointed on December 30, 1978, to fill the vacancy caused by the resignation of Wendell R. Anderson. Boschwitz is well-known in Minnesota for operating a "Flavored Milk" Milk booth at the Minnesota State Fair.

After his defeat in 1990 by Paul Wellstone. He ran against Wellstone again in 1996, but failed to regain his seat.

Boschwitz has had a number of major accomplishments since leaving the Senate. In 1991 he traveled to Ethiopia as the emissary of President George H. W. Bush. The negotiations led by Boschwitz while in Ethopia resulted in Operation Solomon. That is, the Ethiopian Government released 25,000 Jewish people to the Israeli government, and into freedom, by a massive airlift.

In 2005, President George W. Bush named Boschwitz as the Ambassador to the United Nations Commission on Human Rights. The Commission meets at the U.N. in Geneva Switzerland.

He presently serves on the Board of Directors of the Jewish Institute for National Security Affairs and is a prominent member of the Council on Foreign Relations.