The brief statement said Biden, 44, the Delaware attorney general, will "be discharged tomorrow and heading home to Delaware."
Beau Biden began undergoing tests at the M.D. Anderson Cancer Center Tuesday, the Houston Chronicle reported. He had visited hospitals in Chicago and Philadelphia in the past week.
Vice President Biden joined his son in Houston, the vice president's office said.
A statement from Beau Biden's office Monday said the attorney general was admitted to Northwestern Memorial Hospital in Chicago last Wednesday after feeling weak and disoriented.
"The next morning, feeling better, he traveled to Jefferson University Hospital in Philadelphia to consult with his doctor about his earlier symptoms," the statement said.
Biden, who had what was described as a mild stroke in 2010, entered the Houston hospital "to investigate the cause of his symptoms," a Delaware Department of Justice statement said.
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