He has one season remaining on the three-year, $21 million contract extension ($7 million average annual value) he signed with the Golden Knights on July 13, 2018.
Following the trade, Fleury's agent, Allan Walsh, said Fleury was not made aware of it and would be "taking time to discuss his situation with family and seriously evaluate his hockey future."
Bowman said he was not nervous that Fleury needed some time after the trade.
"He has (three) young children, I have kids as well, and it's a tough life to be a player, and I think it's probably obvious that it was a surprise for him when the trade went down," Bowman said. "From my first conversation with him, I think it was consistent. He said, 'Look, thanks so much for the call,' [and] he just talked about how, 'I just need time to get through these things. If you can have a little patience, that'd be great,' and I said, 'Not a problem at all.' I put myself in his shoes. Once we had that conversation, we were willing to give him the time he needed to process through everything."
Fleury confirmed he will join the Blackhawks in a video posted on their Twitter account Sunday.
"Hey Chicago, it's Marc. I just want to let you know I'm in," Fleury said. "Let's get to work."