Schiano coached Tampa Bay for two seasons, going 4-12 in 2013. The mark tied for the third-worst in the NFL behind the Houston Texans and Washington Redskins. Those teams have also made coaching changes in recent weeks.
The Buccaneers were 7-9 in Schiano's first season. He previously coached on the collegiate level at Rutgers.
Dominik had been the Tampa Bay general manager since January 2009. The team has had one winning season -- 10-6 in 2010 -- since then. He had been with the Buccaneers since June 1995.
"The results over the past two years have not lived up to our standards and we believe the time has come to find a new direction," Buccaneers Co-Chairman Bryan Glazer said in a statement.
"Mark has been a valued member of our organization for two decades and we respect the passion he showed for the Buccaneers during his time here. We thank Greg for his hard work and effort the past two seasons but we feel these moves are necessary in order to achieve our goals," said.
Tampa Bay lost its first eight games and also the last three, however, much of the news from the Buccaneers this season was generated by the release of former starting quarterback Josh Freeman.
Freeman opened the year starting the first three games but was benched. Conflict between Freeman and Schiano led to Freeman skipping a team photo shoot. When the Bucs were unable to trade Freeman, who eventually signed with the Minnesota Vikings, it was disclosed that Freeman was in the NFL's substance-abuse program. The NFLPA alleged Schiano leaked that information.