Growing up in Southern California, Baxter started his career at Disneyland at the age of 17, scooping ice cream on Main Street, U.S.A.. After several years of odd jobs at the park, he garnered attention through a portfolio of attraction concepts and was hired at WED Enterprises (now known as Walt Disney Imagineering). His first project roles were relatively minor, but he was eventually given extensive creative control of Big Thunder Mountain Railroad. After this, he continued to be assigned high-level roles in Imagineering projects.
He retired from the company in 2013, but continues to be a consultant for future Imagineering projects.
Projects that Baxter was responsible for include:
- Big Thunder Mountain Railroad (Opened in 1979)
- The re-design of Disneyland's Fantasyland (Opened in 1983)
- The original Journey Into Imagination pavilion (Opened in 1983)
- The Disney Gallery (Opened in 1987)
- Splash Mountain (Opened in 1989)
- Disneyland Paris (Opened in 1992)
- Indiana Jones Adventure: Temple of the Forbidden Eye (Opened in 1995)
- The re-design of Disneyland's Tomorrowland (Opened in 1998)
- Finding Nemo Submarine Voyage (Opened in 2007)
- The re-design of Disneyland's Sleeping Beauty Castle Walkthrough (Opened in 2008)
- The current incarnation of Great Moments with Mr. Lincoln (Opened in 2009)
Never-built projects that Tony personally supervised include a re-design of Disneyland's Tomorrowland called Tomorrowland 2055 and a new land for Disneyland called Discovery Bay. (However, Discovery Bay was a source of inspiration for Discoveryland--Disneyland Paris' version of Tomorrowland.)