The Chargers need depth on the defensive line due to the loss of tackle Jamal Williams, who is out for the season with a triceps injury.
Hart had spent six years with the Chargers, starting in 33 games over the past three seasons. He started three games for San Diego this season.
According to a source, Hart was surprised by the move. But the decision may have been foreshadowed in the past few weeks, as Chargers coaches were removing him from some of the team's nickel packages for passing situations.
Hart's departure means rookie sixth-round pick Kevin Ellison could see more playing time.
Hart, 32, started his career with the Philadelphia Eagles before moving on to the Chargers.
Scott, a seven-year veteran, joined the Chargers last September and appeared in four games. He was released at the conclusion of training camp.
In their last game, the Chargers fell behind Pittsburgh 28-0 before losing 38-28. The Chargers allowed 497 yards of offense.
ESPN.com senior NFL writer John Clayton, ESPN.com AFC West reporter Bill Williamson and ESPN NFL Insider Adam Schefter contributed to this report. Information from The Associated Press was used in this report.