The Cowboys made the announcement Wednesday.
Bledsoe, who has been with the Buffalo Bills the past three years, previously played nine years for New England, four while Parcells coached the Patriots.
The 33-year-old quarterback was officially released by the Bills Tuesday.
Bledsoe, who will compete for the No. 1 quarterback job with Drew Henson, said recently: "I just don't see myself ever being a backup in this league."
Vinny Testaverde, 41 was the Dallas starter for all but one game last season. The Cowboys finished with a record of 6-10.
Bledsoe, who passed for 2,932 yards and 20 touchdowns with 16 interceptions in 2004, has thrown for 39,808 yards in his NFL career, 10th on the all-time list. His other career totals include 221 touchdowns and 181 interceptions.