The Florida Department of Highway Safety and Motor Vehicles (HSMV) states that Florida Statutes define "rebuilt vehicle" as a motor vehicle or mobile home built from "salvage or junk."So yes this type of branded title is legal in Florida.
You can review the HSMV's procedures on obtaining a salvage and a rebuilt title by visiting their website page regarding titles and then scroll to bottom of the page and click the link "DMV Procedures Manual." Click on Section 1 Title and Lien and review Procedures TL-35, TL-36 and TL-37.
Before purchasing a rebuilt item it is generally recommended to have it thoroughly checked out by your own mechanic. You also should check to see if the car can be insured since many insurance companies underwriting rules do not allow them to write policies for cars with salvage or rebuilt titles.