Pearson, 24, appeared in a career-high 80 games this season for the Kings. He recorded career highs in goals (24) and points (44), game-winning goals (five), power-play goals (three), short-handed goals (one) and short-handed points (two).
The 24-year-old former first-round draft pick won a Stanley Cup ring in 2014, scoring 12 points in 24 postseason games. He would have been a restricted free agent this summer.
Pearson says negotiations on his new deal picked up three weeks ago. Rob Blake replaced Dean Lombardi as the Kings' general manager last month.
Bishop, who will be an unrestricted free agent this summer unless Dallas signs him before July 1, played just seven games after the Kings acquired him as a backup for Jonathan Quick. Los Angeles failed to make the playoffs.
Information from The Associated Press was used in this report.