Wideman had 11 goals and 35 assists in 82 games for Washington last season. He was eligible to become an unrestricted free agent Sunday, but agreed to a five-year contract with Calgary on Wednesday worth $5.25 million per year, according to the Flames.
Henry had two goals, nine assists and 97 penalty minutes in 68 games in the AHL last season. He also can enter free agency Sunday.
The move comes one day after Washington named Adam Oates its new head coach.
Information from The Associated Press was used in this report.