Joseph was born in Hallandale, Florida. He played high school football at Hallandale High School. While there he was a four-year starter at both guard and defensive line and played in a school-record 532 plays. During his senior year he was the Broward County Defensive Player of the Year and was awarded All-State after recording 100 tackles and 24 sacks. He was also a two-time 2A state and a national wrestling champion at heavyweight in Florida.
Joseph played college football at Oklahoma. During his freshman year he was named Freshman All-Big 12 by The Sporting News. As a senior he was a consensus First-Team All-Big 12 selection. He finished his career playing in 50 games with 29 starts at guard and 11 starts at left tackle.
Joseph was drafted by the Tampa Bay Buccaneers 23rd overall in the 2006 NFL Draft. During his rookie season he started 12 of 13 games at right guard. In his second season in the NFL he became a full time starter, starting all 16 games at right guard for the buccaneers. He was selected to his first Pro Bowl after the 2008 season as a substitute. He was selected to his second Pro Bowl during the 2011 season.