The trade was announced after Chicago's 5-4 shootout win over Phoenix on Thursday night.
The 27-year-old Versteeg, a member of the Blackhawks' 2010 Stanley Cup championship team, has two goals and five assists in 18 games this season with Florida.
Versteeg had 20 goals and 24 assists in 79 regular-season games with the Blackhawks in 2009-10, then added six goals and eight assists in 22 playoff games during the team's run to the Stanley Cup. He had a career-high 22 goals and 53 points with Chicago in 2008-09.
Obviously there's a lot of expectations around me but it's something I try not to focus on. I'm just trying to go out there, be myself on the ice every day, try to get better, be myself around the guys in the locker room. I think that's what's made me successful and the person that I am.
— Sabres forward Jack Eichel on transitioning from college hockey to the NHL