Upon completion of his military service, he entered private practice with the law firm of Wright, Gilbert and Jones in Columbus, Ohio.

His judicial career began with his election to the Franklin County Common Pleas Court in 1970, where he served as a judge in the general division for 14 years.

He defeated incumbent Justice James P. Celebrezze in November 1984 to win election to his first term on the Ohio State Supreme Court and was re-elected in 1990.

In addition to his judicial and legal activities, Wright was appointed by Governor Bob Taft to serve on the Ohio Chemical Dependency Professionals Board[permanent dead link‍] from 2003 to 2006 and, at the time of his death, he was serving on the Ohio Public Defender Commission pursuant to an appointment from the Supreme Court.

Wright's legacy includes participation with other lawyers and judges in establishing one of the first efforts in the nation to address substance abuse in the legal profession.