Frondell was selected as third by Chicago in the NHL draft earlier in the summer.
According to Chicago, the three-year contract is for 975,000 dollars per season, a total of approximately 28 million kronor over three years.
Frondell, 18, made great success when Djurgården took the step up to SHL. He accounted for 25 points, 11 goals + 14 assists, in 29 regular season matches and was named "Rookie of the Year" in Hockeyallsvenskan.
During the night to Tuesday, teammate Victor Eklund signed a rookie contract with New York Islanders. Eklund was selected as number 16 in the draft.
Frondell has previously stated that he intends to play for Djurgården in SHL the coming season.
