Carpenter, 28, had career-best marks of 13 assists and 18 points in 68 games for the Golden Knights in 2018-'19, when he also had five goals. Carpenter also won 52.6 percent of his faceoffs.
Carpenter played in 17 playoff games in 2017-'18 as the Golden Knights advanced to the Stanley Cup Final. He entered the NHL with the Sharks in 2014.
Kampf, 24, set career-highs with 15 assists and 19 points in 63 games for the Blackahwks last season, when he also had four goals. He originally joined Chicago as a free agent in May 2017.
His new deal runs through the 2020-'21 season.