Stoll's three-year deal is expected to be worth $9.75 million, a source told ESPN.com's Pierre LeBrun. Fraser will get a two-year deal worth $1.65 million, the source said.
The Kings have the entire core of their first championship team under contract except power forward Dustin Penner.
Stoll, who turns 30 on Sunday, is the Kings' third-line center and faceoff specialist. He also plays extensively on the Kings' penalty kill while providing veteran leadership.
Stoll has become a fan favorite while spending the past four seasons with Los Angeles, which acquired him in a 2008 trade with Edmonton. Although he matched his career low with 21 points in the regular season, he contributed five points in the playoffs, including the series-winning overtime goal in the first round to knock out Presidents' Trophy-winning Vancouver.
Fraser is a gritty, defense-minded forward who played extensively for the Kings on their depth lines before appearing in 18 playoff games. He scored only one goal in the postseason, but it was Los Angeles' first goal of the Stanley Cup finals, kicking off the Kings' victory over New Jersey in Game 1.
Fraser, who also won a championship in 2010 with Chicago despite playing in just three postseason games for the Blackhawks, is one of Los Angeles coach Darryl Sutter's favorite players for his no-nonsense work ethic. The Kings acquired Fraser last summer from Edmonton for center Ryan Smyth, who demanded a trade from the Oilers.
Penner is the only major contributor to the Kings' Cup run who is still slated to be an unrestricted free agent on July 1. Los Angeles is scheduled to meet with representatives for Penner, who is eager to return and has acknowledged he would consider taking less than his full market value for the chance to defend the second Stanley Cup title of his career.
Information from ESPN.com's Pierre LeBrun and The Associated Press was used in this report.