The 22-year-old restricted free agent was fifth on the Blackhawks with 24 points (nine goals, 15 assists) in 52 games last season.
"Brandon's ascension to a regular role last season provided a huge boost to our team," Blackhawks general manager Stan Bowman said. "We were quite pleased with the growth he showed in his game and ability to handle tougher assignments. His continued development at this level will allow him to be a valuable contributor to our offense moving forward."
Hagel had been drafted by the Buffalo Sabres in the sixth round (No. 159) of the 2019 NHL Draft but signed with the Blackhawks as a free agent Nov. 5, 2018. He has scored 24 points (nine goals, 15 assists) in 53 games. He played one game with Chicago in 2019-20.