The couple laid a wreath at the site in a solemn ceremony also attended by Philadelphia Mayor Jim Kenney.
"Today, we honor the service of those who have worn the uniform of the Armed Forces of the United States," Joe Biden said in a statement on Twitter.
"To our proud veterans -- I will be a commander in chief who respects your sacrifice, understands your service, and will never betray the values you fought so bravely to defend."
Joe Biden's oldest son, Beau Biden, was a major in the Delaware Army National Guard and was deployed to Iraq. The younger Biden died of brain cancer in 2015.
"If there's anybody who understands what veterans go through, it's this family," a speaker at the Philadelphia event said of the Bidens.
Joe Biden said his family prayed every night and morning for Beau Biden's safety.
"It was hard. It hurt. These are challenges most American families never have to face," he said. "And yet, Jill and I were constantly in awe when visiting with wounded service members at Christmas or hosting veterans in our home for dinners, at the pride our military members and veterans feel in their service, and at their matchless sense of duty.
"They are the absolute best of our country."