Both teams swapped future sixth-round and seventh-round picks as part of the deal, giving the Chiefs higher picks in the two rounds.
Moore's 2024 season came to an end with a calf injury after playing in six games.
The 24-year-old was selected in the second round of the 2022 NFL Draft by the Chiefs. Moore posted 250 yards on 22 receptions in 16 games (three starts) during his rookie year, then 244 yards and a touchdown on 21 receptions (14 games, eight starts) a year later in 2023.
San Fran are in desperate need of receiver help. Demarcus Robinson was officially suspended on Wednesday for the first three games of the season for violating the substance abuse policy.
Star receiver Brandon Aiyuk is currently out with an injury as is other starting receiver Jauan Jennings. Backups Jordan Watkins and Jacob Cowing are also dealing with injuries.