The Kings announced the flurry of signings Friday.
Zatkoff is a former Kings prospect who is expected to replace Jhonas Enroth as Jonathan Quick's backup. Zatkoff won the Stanley Cup with Pittsburgh this summer, playing in 14 regular-season games and two playoff games.
Latta was a free agent after Washington declined to make him a qualifying offer. The grinding forward has 17 points in 113 career games with the Capitals.
Gilbert is a 10-year NHL veteran who scored two points in 45 games for Montreal last season while enduring the first major injury problems of his long career.
Trotman has played three seasons for the Boston Bruins.