Since little to no historical evidence exists on the creator of Tai Chi Boxing, it's history is taken from legend.
Zhang San Feng of the 13th Century was said to have created Tai Chi Boxing in the Purple Summit Temple on Wudang Mountain. It is said he witnessed a fight between a snake and a crane and this inspired him to create Tai Chi Chuan. This would make Tai Chi Chuan at the least about 700-800 years old.
Zhang San Feng taught this fighting art to Taiyi Zhenren, which was passed down to Ma Yun Cheng, then to the "Two Saints" Mi Deng Xia and Guo Ji Yuan. Then passed down to Zhang Song Xi who in turn taught Tai chi Boxing to the Chen Family of Chen village. Though the Chen family maintains that Tai Chi Boxing was created in Chen village.
Then Chen Family Tai Chi Chuan was taught to Yang Lu Chan who created Yang style Taijiquan, who then taught Wu Yu Xiang who created Wu style Tai Chi Chuan. Taijiquan was then still passed down from Wu and Yang Lu Chan's sons and several other styles of Tai Chi Boxing were developed, including Hao, Sun, Li, Zhaobao Styles of Taijiquan.