State television said Tantawi, who ruled Egypt for more than a year after the revolution that toppled former president Hosni Mubarak, was replaced by Abdel Fattah al-Sissi.
Armed forces chief Sami Anan was also retired, a week after a deadly attack on the Egyptian military in the lawless Sinai peninsula, the state broadcaster said.
Morsi appointed judge Mahmud Mekki as his deputy, the official news agency MENA reported, making him only the second vice president to be named in Egypt in 30 years.
Mubarak, who was ousted in a popular uprising last year, named his spy chief Omar Suleiman as vice president just days before he was forced to step down.