Eight people were injured, two of them seriously, The Local.de reported. The worker who died was operating an excavator, which caught fire when the bomb went off.
Euskirchen, a town of 55,000 about 19 miles southeast of Cologne and 25 miles from the Belgian border, is in an area targeted by British and U.S. bombers during the war because it was the center of German heavy industry. Unexploded bombs are still turning up.
The construction site is on Alfred Nobel Strasse, a street named after the inventor of dynamite.
The explosion was heard in Bonn, almost 20 miles away, police told Der Spiegel's website. Windows shattered almost 4 miles away.
"There was a huge blast wave. In the vicinity of the accident site and surrounding streets, home windows shattered and garage doors were pushed in," a police spokesman said.