The 30-year-old Handzus, who has played eight NHL seasons, will earn US$16 million over four years. The 28-year-old Preissing, a three-year NHL veteran, will be paid $2.75 million per season.
The Kings also signed 28-year-old left wing Kyle Calder to a $5.5-million, two-year contract, and 28-year-old left wing Ladislav Nagy to a one-year deal worth $3.75 million.
"I think today we're a better hockey team," Kings general manager Dean Lombardi said on a conference call. "We got some good hockey players. I might look at one other thing. We certainly have the flexibility of going forward after this year."
The Kings came up empty Sunday on the first day of the free-agent signing period, but Lombardi said Monday made up for it.
"I'm glad we didn't have to fall to Plan C," he said. "Once the big boys went, so to speak, we were ready. I'm glad we did move quickly.
"We're sitting here today, the most important thing is we're looking at cap space in years two and three. That's what I'm keeping my eye on."
Lombardi called Handzus "the key guy."
Handzus played only eight games for the Chicago Blackhawks last year before sustaining a season-ending knee injury. He played previously with the St. Louis Blues, where he was a teammate of Nagy's in 2000-01, the Phoenix Coyotes and the Philadelphia Flyers.
"With the chemistry between the two as players, both Nagy and Handzus saw an opportunity to play together again in a market with a team committed to winning," said agent Matt Keator, who represents both players. "Chicago was very professional with Michal but L.A. offered more term-years which is important to him coming after his injury."
Handzus' best season was in 2003-04 with the Flyers, when he had 20 goals and 38 assists. Lombardi said he wasn't concerned about Handzus' knee.
"Michal might not be the sexy name, so to speak," Lombardi said. "People who know hockey really appreciate this guy. He's a pro's pro."
Nagy has played for St. Louis, Phoenix and Dallas. He was with the Coyotes and Stars last season, getting 12 goals and 43 assists in 80 games.
Preissing played for the San Jose Sharks for two seasons before joining the Ottawa Senators, where he had seven goals and 31 assists in 80 games last season.
Calder played six seasons for the Blackhawks, and split last season between the Flyers and Detroit Red Wings, getting 14 goals and 21 assists in 78 games. He had his best season with Chicago two seasons ago with 26 goals and 33 assists in 79 games.