The move is another designed by Chicago to increase the amount of cap space they will have able to use in their restructure that will be undertaken in the off-season.
The Georgian forward Shengalia won't be used much by the Bulls and will almost definitely be released at the end of this season. Point guard Teague however is owed $1.1 million next season and then there are the team option years on his rookie deal after that.
Teague was the back up to Derrick Rose at Chicago, but even despite the stars injury he still did not play. Teague last saw some NBA action on Christmas Day and that was only for two minutes.
At Brooklyn, Teague will be an understudy to the returning Deron Williams at point, allowing for Shaun Livingston to line up at the 2.
All in all however, this is just another move to further set up the Bulls with a great pick in the draft and a big run at free agency. It will be fun to see what they can do.