Each pick is in the 2019 draft. The teams announced the trade Monday before the Kings faced the defending Stanley Cup champion Washington Capitals.
Thompson has four goals and two assists in 53 games for Los Angeles this season. He has won 53.3 percent of his faceoffs, which ranks 34th in the NHL. The 34-year-old is a pending free agent who carries a $1.65 million salary-cap hit for the rest of the season.
The fourth-round pick the Kings got from the Canadiens is the Calgary Flames' selection. The fifth-round pick they sent to Montreal with Thompson is Arizona's selection.