The Bulgarian champions, who did not lose a single league game last season on their way to the title, owe money to several organisations, including the national revenue agency.
As a result they failed to meet the BFU's licensing committee guidelines.
A statement from the Bulgarian Football Union read: "CSKA will not participate in the 2008/2009 UEFA's Champions League as this is a final decision."
CSKA president Alexandar Tomov has accepted responsibility for the exclusion and has stepped down from his post.
On Tuesday he was insulted by fans during a chaotic news conference and hit by a thrown bottle outside the club's Bulgarska Armiya stadium as the club's supporters expressed their anger at Tomov shortcomings in managing the club's finances.
CSKA would have entered the Champions League at the third qualifying stage. They become the second team to be excluded from European competition this week after Porto were also thrown out of the Champions League for match fixing allegations.
The Bulgarians, who have won their national title 31 times, could be also expelled from the domestic top flight and relegated to the third division.
CSKA have said they plan to appeal the decision.
Have your soccer jersey customized with official name and number when you Shop by Player. Please allow additional delivery time on all customizations