Palmer, the brother of Arizona Cardinals quarterback Carson Palmer, worked out for the Bears along with JaMarcus Russell and Trent Edwards in June. A sixth-round draft choice of the Washington Redskins in 2007, Palmer played three games with the Cincinnati Bengals in 2008 and one in 2010. He spent last season with the Jacksonville Jaguars.
The signing was first reported by the NFL Network.
An undrafted free agent in 2012, Blanchard, a native of Lake Zurich, Ill., spent 12 weeks last year on the practice squad. Blanchard had drawn praise from new Bears coach Marc Trestman and offensive coordinator Aaron Kromer for his quick grasp of the offense, decision-making skills and his confidence.
Blanchard completed 16 of 19 passes in two preseason games for 193 yards and an interception. Against the Panthers in the exhibition opener at Carolina, Blanchard scrambled four times for 26 yards.
ESPNChicago.com's Jeff Dickerson and Michael C. Wright contributed to this report.