Born in Butte, Montana to John and Joan Morris, Brian Morris graduated from Butte Central Catholic High School, where he was an All-State athlete, who competed in football, track, and basketball. As a senior in the 1981–1982 academic year, he led the football team to the 1981 state championship game and set school records by rushing 1,640 yards and making 236 carries for 1,732 total yards. In track, he was the 1982 state champion in both intermediate and high hurdles in the high school's first state championship in track.
Earning a scholarship to Stanford University, Morris was a four-year letterman on the Stanford Cardinal football team and was the team's starting fullback in the 1986 Gator Bowl. In the Gator Bowl, Morris made 3 carries for 12 rushing yards and made 3 receptions for 6 yards. In his junior and senior years, he was honorable mention all-Pacific-10 Conference and first team all-academic Pac-10. With 12 pass receptions against UCLA in 1985, Morris is one of the Cardinal's all-time single-game pass reception leaders. Morris earned his Bachelor of Arts in 1986 and his Master of Arts in 1987. As one of only eight students in the United States to earn the NCAA Post-Graduate Scholarship, Morris earned his Juris Doctor with distinction from Stanford Law School in 1992.
After completing his law degree, Morris served as a law clerk to United States Court of Appeals for the Ninth Circuit Judge John T. Noonan, Jr., who had been appointed to the Ninth Circuit by President Ronald Reagan. Completing his clerkship with Noonan, Morris then served as a law clerk to Chief Justice of the United States William Rehnquist.
In 1995, he joined the Iran – United States Claims Tribunal at the World Court, The Hague, Netherlands, to serve as a legal assistant. Returning to Montana, Morris served as an attorney in private practice in Bozeman from 1995 until 1999. He went on to serve as a legal officer at the United Nations Compensation Commission in Geneva, Switzerland.
Again returning to Montana in 2001, Morris served as the Solicitor of the Department of Justice until Montana voters elected him to the Montana Supreme Court in November 2004.
In 2009, Morris wrote the 6–1 decision in Kulstad v. Maniaci, in which the Court ruled in favor of a woman's right to joint custody rights of two children adopted by her same-sex partner during their relationship. In 2010, he wrote the 4–1 decision in Wilson v. Montana that denying an inmate the use of a particular mental illness medication did not violate the criminal's rights.
As a former clerk for Chief Justice Rehnquist, Morris is the only member of the Montana State Bar to have served as a Supreme Court law clerk.
On March 11, 2013, Senator Max Baucus announced that he will recommend that President Obama nominate Morris to fill the vacancy on the United States District Court for the District of Montana caused by Judge Sam Haddon taking senior status, the vacant seat being located in Great Falls. The recommendation was made after a number of candidates were considered by a nine-member Judicial Nominating Commission appointed by Senator Baucus and Senator Jon Tester. On May 23, 2013, President Obama formally nominated Morris to the judgeship. His nomination was reported to the floor by the United States Senate Judiciary Committee on September 19, 2013. Cloture was voted on and agreed to on December 12, 2013 by a vote of 57-40. He was confirmed by the United States Senate in a vote of 75-20 later that same day. He received his judicial commission on December 17, 2013.
Morris and his wife, Cherche, have three sons and one daughter.