The couple, who opted to remain anonymous, selected the cash single-payment value for the jackpot, which totaled $33.05 million before federal withholding taxes.
The winning ticket was validated by Delaware Lottery officials on Friday afternoon.
"I checked my numbers in the newspaper during a break at work, and when I realized I had won, I had the shakes," said the man, who described himself as a laborer, in a written statement. "I was like, I'm done. I'm done for the day!"
His wife was similarly rattled when she heard about their good fortune.
"I said, 'Oh my God!'" she said in the statement. "And I immediately thought, 'What can we do for our family?'"
The ticket was purchased at Cutrona's Liquors in Wilmington.