Seattle made the expected roster moves official eight days before teams can start speaking with potential free agents. Bryant had spent his entire career with the Seahawks after being a fourth-round draft pick in 2008, while Rice signed as a free agent before the 2011 season.
According to the league's transaction report, Rice was released with a "failed physical" designation.
Both were due hefty salaries in 2014 that didn't necessarily match the production they had shown on the field. Rice had struggled with injuries with the Seahawks and was lost for the 2013 season after Week 8 with a knee injury. Bryant was a unique player as a 300-pound defensive end for the Seahawks, but his playing time had diminished.
Seattle should save more than $12 million in salary cap space with the moves. Rice was due $8.5 million in base salary for 2014 and Bryant $4.5 million.
"We want to thank both Red and Sidney for their effort, commitment and contribution to the Seattle Seahawks over the last few years," Seattle general manager John Schneider said in a statement. "These are extremely tough decisions, but we wanted to give them a head start on free agency. We wish them well in the future."
Both moves were expected to happen and are likely the first in a series that will change the makeup of the Super Bowl champions.
Bryant was one of just four players left from before the arrival of Schneider and head coach Pete Carroll. He was given a new contract during the 2012 offseason, but the emergence of Michael Bennett - one of Seattle's top free agent priorities - appeared to make Bryant expendable.
The only players still remaining from the pre-Carroll era are center Max Unger, defensive tackle Brandon Mebane and punter Jon Ryan.
Bryant was also a captain and vocal leader of Seattle's league-best defense. He could be an attractive option in free agency for a team seeking a defensive end that can hold the edge in defending the run in a 3-4 defense.
Rice had not matched the production that came with his big contract, mostly because of injuries. Rice played in 33 games with 31 starts with 97 receptions for 1,463 yards and 12 touchdowns. But his 2011 season was cut short by a concussion and he was unable to finish the 2013 season after suffering an ACL tear in his knee and being placed on injured reserve. Rice led Seattle in receptions (50) and yards receiving (748) during the 2012 season, one of just two seasons in his career that he's played in all 16 regular-season games.
Rice tweeted a goodbye to Seattle fans shortly after his release became official: "The amount of love I have for the #12thman and the Seahawks organization! Thanks for a wonderful experience!"