The community of Sublett was named for John William Sublett who purchased a 1,000 acre tract of land eight miles south of where the City of Arlington is now. There was also a school and road named Sublett. The road remains today, inside the City of Arlington, but the school was consolidated with Mansfield Independent School District (MISD) in about 1950.
The Sublett Post Office was established in 1892, and Charles A. Sublett was the postmaster. The post office dispatched and received mail from Johnson Station. The carrier, Joe Kelly, rode horseback to deliver the mail and earned $75 a month in wages. The mail in Johnson Station, now the City of Arlington, was delivered there by stage coach.
The post office, located in the home of Charles Sublett, was also a general store. Dr. J.H. Hammack also had his office there before moving to Kennedale.
The Rehoboth Cemetery is located in the Sublett Community and many old-timers who have family buried there come for annual reunions. The Rehoboth Cemetery received a state historical marker from the Texas Historic Commission.