Henry Baldwin was born on January 14, 1780 in New Haven Connecticut.

In 1797 at age 17, Baldwin received a doctor of laws degree from Yale University. He was elected to the United States Congress as a member of the Democratic-Republican Party in 1816, representing Pennsylvania, but resigned after six years because of his declining health and failing finances. He strongly supported the election of Andrew Jackson in the election of 1828. After the death of Bushrod Washington in 1829, Jackson nominated Baldwin to the Supreme Court.

Baldwin considered resigning in 1831. In a letter to President Jackson, he complained about the Court’s extension of its powers. Some historians believe that Baldwin suffered from mental illness during this period. However, he continued to serve on the court until his death.

Justice Baldwin was personally opposed to slavery. In the case of Johnson v. Tompkins, 13 F. Cas. 840 (C.C.E.D. Pa. 1833), he instructed the jury that although slavery's existence "is abhorrent to all our ideas of natural right and justice," the jury must respect the legal status of slavery. He was the sole dissenter in the Amistad Case, in which the Court decided to free a ship of illegally imported African slaves.

In another federal case, Justice Baldwin interpreted the Privileges and Immunities Clause of the Constitution. That case was Magill v. Brown, 16 Fed. Cas. 408 (C.C.E.D. Pa. 1833), in which Justice Baldwin stated: "We must take it therefore as a grant by the people of the state in convention, to the citizens of all the other states of the Union, of the privileges and immunities of the citizens of this state." This eventually became the view accepted by the Supreme Court, and remains so.

Justice Baldwin was a friend and admirer of Chief Justice John Marshall, and wrote of Marshall that "no commentator ever followed the text more faithfully, or ever made a commentary more accordant with its strict intention and language." Baldwin was at Marshall's bedside when the old Chief Justice died in 1835.

In 1837, Justice Baldwin authored a treatise titled A General View of the Origin and Nature of the Constitution and Government of the United States: Deduced from the Political History and Condition of the Colonies and States. Baldwin opposed the two prevailing schools of Constitutional interpretation: the strict constructionists and the school of liberal interpretation. Likewise, his views followed a middle course between the extremes of states' rights on the one hand, and nationalism on the other hand.

Justice Baldwin suffered from paralysis in later years and died a pauper, aged 64. Historian William J. Novak of the University of Chicago has written that, "Baldwin’s jurisprudence has been treated rather shabbily by historians."

Baldwin was the great-great-great-great-grandfather of actor Christopher Reeve.

Baldwin died on April 21, 1844 in Philadelphia, Pennsylvania.