Beau Biden, 41, was being treated at Thomas Jefferson University Hospital, a renowned neuroscience hospital in Philadelphia, a day after suffering the stroke.
"He will continue to follow standard protocol and receive medical therapy over the coming days, as is typical for any patient recovering from an event like this," the Delaware Department of Justice said in a statement. "He looks forward to returning to his duties as Attorney General in the near future."
The vice president and his wife, Jill, were in Philadelphia on Wednesday. The White House said the vice president would return Wednesday afternoon to Washington to meet with Karl Eikenberry, the U.S. ambassador to Afghanistan, and host a dinner for Afghan President Hamid Karzai in the evening. Biden is one of the Obama administration's major voices in setting Afghanistan policy.
Outside the hospital Wednesday afternoon, the vice president held up a cheesesteak and yelled to reporters, "My son is doing great!"
Beau Biden was admitted to Christiana Hospital in Newark, Del., on Tuesday morning. Later in the day he was transferred to Thomas Jefferson, about 45 miles away, vice presidential spokeswoman Elizabeth Alexander said. The White House said earlier that he would undergo further observation and examination there.
Thomas Jefferson is the only dedicated hospital for neuroscience in the Philadelphia region, its website says, and the largest center in the region for treating strokes and aneurysms.
The hospital is certified by the Joint Commission in Stroke as a Primary Stroke Center. It is one of a few hospitals in the Philadelphia area to be cited for excellence by The American Stroke Association and American Heart Association.
Thomas Jefferson officials declined to comment, referring questions to the vice president's office.
In a statement issued Tuesday through the White House, Christiana's Dr. Timothy Gardner said Biden was in good spirits and was talking with his relatives. The doctor said Biden was fully alert and in stable condition and had full motor and speech skills.
Beau Biden returned last year from a yearlong deployment to Iraq with his Army National Guard unit. He was a captain and military lawyer in the 261st Theater Tactical Signal Brigade. He had considered running this year for the Senate seat his father held before becoming vice president, but decided instead to run for re-election as attorney general.
Beau Biden announced in January that he wouldn't run for Senate, saying he needed to focus as attorney general on the high-profile criminal case against a pediatrician prosecutors say may have molested more than 100 children over the past decade.
The decision left vulnerable the seat Joe Biden held for 36 years. The elder Biden was away from that seat for seven months in 1988 after undergoing surgery for brain aneurysms.
More than a decade earlier, in 1972, he lost his wife and infant daughter when a tractor-trailer broadsided their station wagon when they were getting a Christmas tree. Beau and his brother, Hunter, were critically injured but recovered.
Beau Biden, who is married with two young children, has worked as an attorney in private practice. He also worked for the Department of Justice between 1995 and 1997 and as an assistant U.S. attorney from 1997 to 2002.
Associated Press writers JoAnn Loviglio in Philadelphia, Randall Chase in Newark, Del., Ben Nuckols in Baltimore, Brian Witte in Annapolis, Md., and Nafeesa Syeed and Julie Pace in Washington contributed to this report.