The six-foot-five Alexeev scored 10 goals and had 11 assists in 63 games with the Lightning this season. He was the Lightning's first-round pick and No. 8 overall in the 2000 draft. He's appeared in 144 NHL games with 18 goals and 17 assists.
Stewart was acquired by the Blackhawks off waivers from the Pittsburgh Penguins on Oct. 26. He has two goals and three assists in 37 games.
It was the third trade completed by Chicago this week. On Monday, the Blackhawks traded centre Bryan Smolinski to Vancouver for a second-round pick and were part of a three-way deal with Philadelphia and Detroit in which they ended up with centre Jason Williams.