The former Air Force commander and civil aviation minister was Hosni Mubarak's last prime minister and was dumped in the face of protests after the president's ouster.
Shafiq, 70, scores points by presenting himself as a strongman who will stabilize the country, promising to restore law and order within 24 hours of taking office.
His campaign for the runoff has focused on warning against the Muslim Brotherhood, drawing on the fear among many Egyptians of its rising power and what they see as its drive to dominate the state and change their lifestyle with stricter Islamic rules.
Opponents view Shafiq as the military's favorite.
In the first round, Shafiq came in second, winning a surprisingly high 5.3 million votes or nearly 24% of the total.
The candidate of the Muslim Brotherhood, Egypt's strongest political movement, was educated as an engineer in southern California.
Elected to parliament several times under Mubarak's rule, Morsi, 60, is not seen as the group's most charismatic figure but has its organizational power behind him.
The Brotherhood's platform promises to reform corrupt institutions, put the state on an "Islamic basis" and apply more Islamic law.
In the second round, Morsi sought to appeal to revolutionaries his group alienated in its quest for political power, and has campaigned as the only candidate that will prevent the return of Mubarak's regime.
In the first round, Morsi came in first, winning a surprisingly low total of 5.6 million votes or nearly 25%.