Neither move was a surprise.
The Bucs dealt McCown to the Jaguars for a late-round conditional draft pick in 2010, a source with knowledge of the situation told NFL.com's Steve Wyche. Tampa Bay had been shopping McCown for more than a week, and Jacksonville was looking to find a solid backup to starter David Garrard.
Johnson completed 7 of 17 passes for 182 yards and one touchdown with one interception in Friday night's preseason finale against the Houston Texans. For much of training camp, Morris suggested that Johnson might be among the best 53 players on the team.
"We want to keep the best 53, and Josh went out (Friday night) and proved he can move the football, and when he's out there he can be productive, he can learn and he can go without a whole bunch of reps," Morris said after the game. "That's a big-time quality in this league.
"When he gets his opportunity to go play, he plays well and fights his way to the top. That's what I want this team to be built on."
Bryant was released even though his 83.1 field-goal success rate in four seasons is the best in franchise history. He injured his right hamstring in practice last month and didn't kick in the preseason.
The Bucs also placed offensive tackle Xavier Fulton on injured reserve and waived/injured safety Donte Nicholson.
Safety Tanard Jackson, who has started every game since entering the NFL in 2007, was placed on the reserve/suspended list. The NFL suspended Jackson for the first four games of the regular season for violating the league's substance-abuse policy.
Jackson's suspension leaves Tampa Bay's roster at 52 players, meaning a roster replacement will be signed in the next few days.
In addition to releasing Bryant, an eighth-year pro who scored a team-record 131 points last season, the Bucs waived safety Steve Cargile, offensive tackles James Lee and Anthony Alabi, linebacker Bo Rudd, cornerbacks Kyle Arrington and Darrell Hunter, defensive tackles Rashaad Duncan and Chris Bradwell, center Rob Bruggeman, fullback Jameel Cook, defensive ends Louis Holmes and Jarriett Buie, tight ends Jason Pociask and Ryan Purvis, running back Kareem Huggins, and wide receivers Patrick Carter, Cortez Hankton, Marcus Maxwell and Mario Urrutia.
Bryant, 34, signed with Tampa Bay as a free agent in 2005. Among his accomplishments was kicking the second-longest game-winning field goal in NFL history, a 62-yarder against the Philadelphia Eagles in 2006.
Bryant converted 32 of 38 field-goal attempts and made three game-winning kicks last season.
The Associated Press contributed to this report.