Duncan used a city UPS account to ship the stolen goods to the Willis' business in Russellville, prosecutors contend.
"The fraud alleged in this indictment cost the city crucial funds that might have benefitted the taxpayers in other ways," U.S. Attorney Zane David Memeger said in a statement.
The city's Office of Inspector General began the investigation in September 2011, and the FBI joined two months later.
"Collaboration is the key to fighting public corruption in Philadelphia," Inspector General Amy Kurland said. "Oftentimes, cases like this start with tips from city employees who have the courage to do the right thing."
The indictment does not say how the investigation started or explain Duncan's tie to the Arkansas couple.
Each is charged with fraud and aiding and abetting. Derek Willis, 48, and Anita Willis, 34, face additional charges of obstruction and perjury for allegedly trying to destroy evidence and lying to the grand jury.
Agents arrested the couple Wednesday.
Duncan, who was fired from his city job after the investigation started last year, is expected to surrender to authorities this week. He had no listed phone number and could not be reached for comment.
Contact John P. Martin at 215-925-2649, at firstname.lastname@example.org or @JPMartinInky on Twitter.