"As a result of those discussions, the parties have decided to resolve the pending grievances. The resolution of this matter is subject to a confidentiality agreement so there will be no further comment by any party."
Quarterback Kaepernick, 31, began his protests in the 2016 pre-season, initially remaining on the team bench during the anthem before refining his approach and kneeling on the sideline, where he was soon joined by then team-mate Reid.
Players throughout the league joined in with the protests during the 2016 and 2017 seasons, with the movement intensifying after President Donald Trump called for protesting players to be "fired" and referred to them as "sons of b******".
Kaepernick left the 49ers at the end of 2016 and has not played in the NFL since. Reid went unsigned in free agency ahead of the 2018 season, but was later snapped up by the Carolina Panthers, where he has since earned a three-year contract extension.
The NFL Players' Association welcomed the resolution of the grievances.
"We are not privy to the details of the settlement, but support the decision by the players and their counsel," an NFLPA statement read:
"We continuously supported Colin and Eric from the start of their protests, participated with their lawyers throughout their legal proceedings and were prepared to participate in the upcoming trial in pursuit of both truth and justice for what we believe the NFL and its clubs did to them.
"We are glad that Eric has earned a job and new contract, and we continue to hope that Colin gets his opportunity as well."
Kaepernick spent six seasons with San Francisco, in which he threw for over 13,500 yards and 79 touchdowns, and led the team to Super Bowl XLVII in 2013.