It is a key part of a major project for Istanbul that includes a new airport and a canal linking the Black Sea to the Sea of Marmara to bypass the Bosphorus, relieving pressure on the vessel-clogged waterway.
Critics have blasted President Recep Tayyip Erdogan's grandiose projects as wildly excessive and damaging to the environment.
But Erdogan hailed the "star project," at a ceremony attended by several ministers, saying: "Those who think big realise big projects. That's how we set out the road."
But the 16th century sultan, blamed by some for massacring religious minorities, is a controversial figure and the name has enraged many Turks.
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Erdogan defended the name. "We will link Europe with Asia with the Sultan Selim Bridge and this will be our most important message to the world," he said at the ceremony.
The crossing will be open for public use by the end of August, officials said. Heavy trucks will be allowed to cross the bridge, to relieve traffic congestion in the city of 16 million people.
There are already two other bridges across the Bosphorus: the First Bosphorus Bridge, which opened in 1973, and the Fatih Sultan Mehmet Bridge, which was completed in 1988.