The robbery happened shortly before 2:30 p.m. Thursday at the PNC Bank at 4725 Kirkwood Highway.
Police got a description of the suspect and began a search.
Soon, troopers began chasing a man who was taken into custody on Armour Drive in the community of Delpark Manor.
That man has been identified as Joseph McCauley, 29, of Wilmington.
McCauley was charged with Robbery 2nd Degree and Wearing a Disguise During the Commission of a Felony.
He was committed to Howard R. Young Correctional Institute on $12,000 cash bond.