Baldwin, 50, is the first woman to be elected to the Senate from Wisconsin. Her inclusion means that the number of women members in the Senate will go up to 18, which is also a new record.
Baldwin's victory left her supporters ecstatic. Katie Belanger, the executive director of Fair Wisconsin, a civil rights organisation said it was incredible to have a person like Baldwin, who was "out and truly represents Wisconsin".
During the poll campaign, however, Baldwin's sexual orientation was not much registered with voters. The Democrat also said that it was not a major factor in the race to the Senate.
Baldwin served 14 years in the House of Representatives and was known to be one of the most liberal Democrat leader. She helped in scripting parts of President Barrack Obama's healthcare plan and voted for a climate change law.
The Republicans had targetted Baldwin over these issues. She was also considered an underdog against her 70-year-old opponent Thompson, the four-time Governor and looked as a father figure in Wisconsin after a long career in public life.
Baldwin was moved by the support given by national LGBT groups and environmental organisations who backed her campaign monetarily.