Bork was born in Pittsburgh, Pennsylvania. His father was Harry Philip Bork (1897–1974), a steel company purchasing agent, and his mother was Elisabeth Kunkle (1898–2004), a schoolteacher. He was married to Claire Davidson from 1952 until 1980, when she died of cancer. They had a daughter, Ellen, and two sons, Robert and Charles. In 1982 he married Mary Ellen Pohl, a Roman Catholic religious sister turned activist.

Bork attended the Hotchkiss School in Lakeville, Connecticut and earned bachelor's and law degrees from the University of Chicago. While pursuing his bachelor's degree he became a brother of the international social fraternity of Phi Gamma Delta. While pursuing his law degree he served on Law Review. At UC he was awarded a Phi Beta Kappa key with his law degree in 1953 and passed the bar in Illinois that same year. After a period of service in the United States Marine Corps, Bork began as a lawyer in private practice in 1954 and then was a professor at Yale Law School from 1962 to 1975 and 1977 to 1981. Among his students during this time were Bill Clinton, Hillary Rodham Clinton, Anita Hill, Robert Reich, Jerry Brown and John R. Bolton.

Bork is best known for his theory that the only way to reconcile the role of the judiciary in the U.S. government against what he terms the "Madisonian" or "counter-majoritarian" dilemma of the judiciary making law without popular approval is for constitutional adjudication to be guided by the framers' original understanding of the United States Constitution. Reiterating that it is a court's task to adjudicate and not to "legislate from the bench," he has advocated that judges exercise restraint in deciding cases, emphasizing that the role of the courts is to frame "neutral principles" (a term borrowed from Herbert Wechsler) and not simply ad hoc pronouncements or subjective value judgments. Bork once said, "The truth is that the judge who looks outside the Constitution always looks inside himself and nowhere else."

Bork built on the influential critiques of the Warren Court authored by Alexander Bickel, who criticized the Supreme Court under Warren for shoddy and inconsistent reasoning, undue activism, and misuse of historical materials. Bork's critique was harder-edged than Bickel's, however, and he has written, "We are increasingly governed not by law or elected representatives but by an unelected, unrepresentative, unaccountable committee of lawyers applying no will but their own." Bork's writings have influenced the opinions of conservative judges such as Associate Justice Antonin Scalia and former Chief Justice William Rehnquist of the U.S. Supreme Court, and sparked a vigorous debate within legal academia about how the Constitution is to be interpreted.

At Yale, he was best known for writing The Antitrust Paradox, a book in which he argued that consumers were often beneficiaries of corporate mergers, and that many then-current readings of the antitrust laws were economically irrational and hurt consumers. Bork's writings on antitrust law, along with those of Richard Posner and other law and economics and Chicago School thinkers, were heavily influential in causing a shift in the U.S. Supreme Court's approach to antitrust laws since the 1970s.

Bork served as Solicitor General in the U.S. Department of Justice from June 1973 to 1977. As Solicitor General, Bork argued several high profile cases before the Supreme Court in the 1970s, including 1974's Milliken v. Bradley, where Bork's brief in support of the State of Michigan was influential among the justices. Chief Justice Warren Burger called Bork the most effective counsel to appear before the Court during his tenure. Bork hired many young attorneys as Assistants who went on to have remarkable careers, including Judges Danny Boggs and Frank H. Easterbrook as well as Robert Reich, later President Bill Clinton's Secretary of Labor.

On October 20, 1973 Solicitor General Bork was instrumental in the "Saturday Night Massacre", U.S. President Richard Nixon's firing of Watergate Special Prosecutor Archibald Cox, following Cox's request for tapes of his Oval Office conversations. Nixon initially ordered U.S. Attorney General, Elliot Richardson, to fire Cox. Richardson resigned rather than carry out the order. Deputy Attorney General William Ruckelshaus considered the order "fundamentally wrong" and also resigned, making Bork acting Attorney General. When Nixon reiterated his order, Bork complied and fired Cox. He remained acting Attorney General until the appointment of William B. Saxbe on December 17, 1973.

Bork was a circuit judge for the United States Court of Appeals for the District of Columbia Circuit between 1982 and 1988. He was nominated by President Reagan on December 7, 1981, was confirmed by the Senate on February 8, 1982, and received his commission on February 9, 1982.

One of his opinions while on the D.C. Circuit was Dronenburg v. Zech, 741 F.2d 1388, decided in 1984. This case involved James L. Dronenburg, a sailor who had been administratively discharged from the Navy for engaging in homosexual conduct. Dronenburg argued that his discharge violated his right to privacy. This argument was rejected in an opinion written by Bork and joined by (now U.S. Supreme Court Justice) Antonin Scalia, in which Bork critiqued the line of Supreme Court cases upholding a right to privacy. In rejecting Dronenburg's suggestion for a rehearing en banc, the D.C. Circuit issued four separate opinions, including one by Bork (again joined by Justice Scalia), who wrote: "no principle had been articulated [by the Supreme Court] that enabled us to determine whether appellant's case fell within or without that principle."

President Reagan nominated Bork for Associate Justice of the Supreme Court on July 1, 1987. A hotly contested United States Senate debate over Bork's nomination ensued. Opposition was partly fueled by strong opposition by civil and women's rights groups concerned with Bork's opposition to the Federal government's right to impose standards of voting fairness upon the states (at his confirmation hearings for the position of Solicitor General, he supported the rights of Southern states to impose a poll tax), and his stated desire to roll back civil rights decisions of the Warren and Burger courts. Bork is one of only three Supreme Court nominees to ever be opposed by the American Civil Liberties Union, along with William Rehnquist and Samuel Alito. Bork was also criticized for being an "advocate of disproportionate powers for the executive branch of Government, almost executive supremacy", which his role in the Saturday Night Massacre exemplified according to his critics.