When Taylor was 2, his family moved to Chillicothe, Illinois. His dad became athletic director of Chillicothe Township High School (now Illinois Valley Central High School) as well as a respected football coach, and both Josh and older brother Ron played quarterback under him. Heavily recruited for his football skills, Josh chose Dartmouth College, and graduated from there with a Bachelors Degree in Sociology. He then received a full scholarship to the University of Denver law school, and earned his juris doctor degree. After earning his law degree, he moved to the west coast.

After earning his Juris Doctorate, he decided to take a year off and work on the Alaskan pipeline. On the way to Alaska he stopped in Los Angeles to visit friends and was offered a job as manager of the Beverly Hills Brakskeller. He spent a year and a half at the restaurant which catered to celebrities and, surrounded by actors and producers, decided to give up a future in the law to pursue acting. After the Bratskellar closed, he worked as a bartender at the Riverside Lounge in Santa Monicca until he snagged his first acting role playing a contemporary cowboy on an episode of Barnaby Jones in 1976. This was quickly followed with roles on The Six Million Dollar Man and The Hardy Boys. In 1977 he took the role of bartender Chris Kostichek on the soap opera "Days of Our Lives." He left the show in 1987 to pursue other roles. In 1988 he starred opposite Barbara Eden in the made for television movie, "The Secret Life of Kathy McCormick," and guest starred on series including "Diagnosis Murder," "Walker: Texas Ranger," "Murder She Wrote," "Matlock," and "LA Law." In 1981 he had his own short-lived detective series, "Riker." He followed this with the pilot of the television version of "The North Dallas Forty," and starred as Mike Hogan on The Hogan Family until 1991. He played Jack McKay on Beverly Hills 90210. In 1997, he returned to Days as the character Roman Brady. In 2004, Roman was murdered by the Salem Stalker (who turned out to be his ex-wife, Marlena) during his and Kate's wedding reception. A few months later, it was revealed that Roman didn't die but was alive on a tropical island called Melaswen (New Salem). He is still appearing on the show.

He has one daughter, Tristan, from his first marriage while in college. He had a long term relationship with dancer/actress Sandahl Bergman in the 80's. On 1999-11-06, he married Lisa Tremblay, a flight attendant he met in 1995.