The move was made hours prior to Buffalo's home game against Atlanta.
"It was nothing more than giving him the opportunity to play," Sabres general manager Darcy Regier said before the game. "We tried to move him with a trade. But, unfortunately, we weren't able to. So this is the next step in helping him resume his career."
Rivet is a 16-year NHL veteran who has a goal and two assists in 23 games this season. He's been the odd-man out in a defensively deep lineup for much of this season, having been a healthy scratch for the past 16 games.
Acquired in a trade with San Jose in the summer of 2008, Rivet is in the final year of a contract that was to pay him $3.5 million. If he goes unclaimed, it's unclear whether Rivet will report to the minors.
"He handled it very well," Regier said. "I give him a lot of credit. He's been very professional."
Rivet had offseason shoulder surgery, and in September, he even raised the prospect that this would be his final season.
He played in Buffalo's first eight games before missing one with an injury. Rivet was then in and out of the lineup for much of the next two months before appearing in nine straight games, including his final one on Jan. 11, in which he had just under six minutes of ice time in a 5-2 loss to Philadelphia.
Despite being a newcomer in Buffalo, Rivet was awarded the team's captaincy following a players' vote during his first season.
Rivet was selected by Montreal in the third round of the 1992 draft, and made his debut with the Canadiens two years later. He spent parts of 12 seasons in Montreal before being dealt to San Jose during the 2006-07 season. Rivet's best NHL season came with San Jose in 2007-08, when he had five goals and a career-best 35 points.
He has 49 goals and 187 assists in 909 career games.
The decision to waive Rivet is the first move the Sabres made under new ownership, coming a day after Terry Pegula closed on a $189 million deal to purchase the team from Tom Golisano. And Rivet's pending departure comes less than a week before the NHL's trading deadline on Monday.