Born in Bladensburg, Maryland to a Swiss father and a German mother, Wirt was privately educated, studied law and was admitted to the bar in 1792. After several years as a lawyer, he became clerk of the Virginia House of Delegates, then chancellor of the Eastern District of Virginia. In 1807, President Thomas Jefferson asked him to be the prosecutor in Aaron Burr's treason trial. President James Monroe named him the ninth Attorney General of the United States in 1817, a position he held for 12 years, through the administration of John Quincy Adams, until 1829.

In June 1830, a delegation of Cherokee led by Chief John Ross selected Wirt on the urging of Senators Webster and Frelinghuysen to defend Cherokee rights before the U.S. Supreme Court. Wirt argued in Cherokee Nation v. Georgia that "the Cherokee Nation a foreign nation in the sense of our constitution and law..." and was not subject to Georgia's jurisdiction. Wirt asked the Supreme Court to null and void all Georgia laws extended over Cherokee territory on the grounds that they violated the U.S. Constitution, United States-Cherokee treaties, and United States intercourse laws.

Although the Court determined that it did not have original jurisdication in this case, the Court held open the possibility that it yet might rule in favor of the Cherokee. Wirt therefore waited for a test case to again resolve the constitutionality of the laws of Georgia. The opportunity came on March 1, 1831, when Georgia passed a law aimed at evicting missionaries, who were perceived as encouraging the Cherokee resistance to removal, from Cherokee lands. The American Board of Commissioners for Foreign Missions, an interdenominational missionary organization hired Wirt to challenge the new law. The decision in Worcester v. Georgia was handed down by Marshall on March 3, 1832, and stated that in the Cherokee Nation, "the laws of Georgia have no force, and...the citizens of Georgia have no right to enter."

After leaving Washington, D.C., he returned to Baltimore, Maryland, was an unsuccessful candidate for President in 1832 as the candidate of the Anti-Masonic party. This was rather ironic because he was, in fact, a Freemason, and even gave a speech at the Anti-Masonic convention defending the organization. In going on to win Vermont, he became the first candidate of an organized third party to carry a state. Wirt practiced law until his death in 1834.

In 1817, Wirt wrote Life and Character of Patrick Henry, a biography of Patrick Henry which contained the supposed text of some of Henry's speeches, many of which had never been published. Some historians have since speculated that some of Henry's phrases that have since become famous, such as "Give me liberty or give me death!" were essentially fabricated by Wirt for this book.

Wirt County, West Virginia (formerly Virginia) is named in his honor.