[3] President Gerald Ford nominated Tjoflat to the United States Court of Appeals for the Fifth Circuit on November 3, 1975, to a seat vacated by Judge John Milton Bryan Simpson.

He was confirmed by the Senate on November 20, 1975, he received his commission the next day and began serving on the court on December 12, 1975.

[2] Following the failure of the Robert Bork nomination in 1987, Tjoflat was placed on the short list of possible nominees for the Supreme Court seat formerly occupied by Lewis F. Powell Jr..[4] Former Governor Claude R. Kirk Jr. pushed for Tjoflat to be nominated after Douglas H. Ginsburg withdrew,[5] but although Florida Senators Lawton Chiles and Bob Graham both said Tjoflat was much more acceptable than Bork,[6] it was always extremely uncertain whether Northeastern Democrats would have found him acceptable,[7] and consequently the seat went to Anthony Kennedy.

In August 2019, Tjoflat informed President Donald Trump that he will take senior status contingent upon the confirmation and appointment of his successor.

[9] In 1995, the Duke Law Journal at the Duke University School of Law published a tribute to Tjoflat that included articles by then-Chief Justice William H. Rehnquist, retired Justices Lewis F. Powell, Jr. and Byron R. White, and Judge Edward R. Becker of the U.S. Court of Appeals for the Third Circuit, among others.