Manager Poyet, his assistant Mauricio Taricco and Oatway were told to stay away from the club pending an internal inquiry in the aftermath of the play-off semi-final defeat by Crystal Palace.
Poyet has since been sacked - although he has said he will appeal against the decision - and replaced by Oscar Garcia, while Taricco had his suspension lifted before leaving by mutual consent last week.
And now former Seagulls skipper Oatway is bringing a 14-year association with the club to an end.
A Brighton statement read: "The club would like to sincerely thank Charlie for his hard work, commitment and dedication since he joined the club in 1999.
"Charlie joined the club as a player in 1999, eventually becoming club captain. During Charlie's successful playing career, he helped the club secure championships in 2001 and 2002 and a play-off victory in 2004.
"Following the end of his playing career, Charlie remained involved with the club working with its charitable arm Albion in the Community.
"In November 2009, Charlie became first-team coach, helping to guide the team to promotion as League One champions in 2011 and a highly creditable fourth-placed finish last season, the club's highest position for 30 years.
"We wish him all the very best for the future and are confident he will have a long and successful career ahead of him."
- Sports & Recreation
- Mauricio Taricco