Cincinnati has signed only one free agent from another club -- quarterback Josh Johnson from Tampa Bay, who also will compete for the job.
Skelton was a fifth-round pick from Fordham in 2010 who started 17 games in three seasons, including six last year. He has completed 53 per cent of his passes for 3,707 yards with 15 touchdowns and 25 interceptions.
The Bengals also signed linebacker Vincent Rey to a new deal on Wednesday. Rey was third in special teams tackles last season and had one sack.