James Burton Carey was born on February 17, 1905, at his family's home in Georgetown, Delaware, the youngest of six children of John Thomas and Mary Burbage Carey. He was graduated from Georgetown High School in 1922. He was graduated from the University of Delaware in 1926, where he was a member of the Sigma Nu fraternity.

After college, Justice Carey settled in Philadelphia where he obtained his law degree from the Temple University evening division in 1931. During law school, he worked during the day for the General Accidental Insurance Company and later the Independence Indemnity Company. He was admitted to the Pennsylvania bar in 1931. In 1936 he became a member of the Delaware bar along with several others who would distinguish themselves in the Delaware judiciary, including: Justice James M. Tunnell, Jr.; Chief Justices Daniel F. Wolcott and Daniel J. Layton; and Chancellor William Marvel. After his admission to the Delaware bar, Justice Carey was a sole practitioner in Georgetown for approximately nine years.

On August 6, 1945, he was appointed by Governor Walter W. Bacon to the Superior Court as resident judge for Sussex County, succeeding Judge Charles Richards, who was nominated to serve as chief justice. After serving his first full twelve-year term, Justice Carey was reappointed to the Superior Court for a second twelve-year term by Governor J. Caleb Boggs.

On May 16, 1963, Justice Carey was nominated by Governor Elbert N. Carvel to the position of justice of the Delaware Supreme Court to fill the seat vacated by Charles L. Terry, Jr. Then-Superior Court Judge Terry was appointed at the same time to serve as chief justice after Chief Justice Clarence A. Southerland retired from the bench. Justice Carey and Chief Justice Terry were both confirmed immediately by the Senate.

Justice Carey served on the Supreme Court until 1974, when he retired to enjoy time with his wife, Marguerite, and his children and grandchildren and to travel. During his service as a member of the Delaware judiciary, Justice Carey authored over three hundred reported opinions. During his tenure on the Supreme Court, Justice Carey chaired the effort to renovate the Sussex County Courthouse on the Circle in Georgetown.

The lawyers of Kent County and Sussex Court honored Justice Carey in 1991 when the Terry-Carey American Inn of Court was created and named for him and his good friend, Charles L. Terry, Jr. Outside the law, Justice Carey was active in the Franklin Lodge #2, where he was a past master, and as a member of the Georgetown Rotary Club. He also served as a member of the vestry of St. Paul's Episcopal Church in Georgetown. His hobbies included playing the piano, at which he as quite accomplished, collecting stamps and tending to his iris garden. Justice Carey died on August 10, 1979, after a long illness.