The 680m (2,230 ft) bridge worth $140M links the city centre with southern neighbourhoods across the Indian Ocean and is expected to ease over-crowding on ferries.
Tanzania’s leader John Magufuli hailed it as a “liberation” for residents in the city of more than four million.
The Chinese firm which built the $140m (£98m) structure says it is East Africa’s longest cable-stayed bridge.
It is also the first toll road in Tanzania. The prices have yet to be set – vehicles and motorcycles will have to pay, pedestrians and bicycle will have free passage.
Correspondents say until now commuters’ only option to cross over the creek to the Kigamboni suburbs was in badly maintained ferries. – and they are often held up for hours because of breakdowns.
Motorists also take their cars on to the ferries, and some have fallen into the sea as the vessels leave as they are not always properly loaded.
The bridge links to an area earmarked in 2010 for an ambitious plan to build a satellite city, known as the Kigamboni New City development.
The government also hopes that it will boost tourism, making it easier for people to go to beaches on the other side of the city.
At a ceremony to open the bridge, Mr Magufuli described the seven-lane cable-stayed bridge as the only one of its kind in central and East Africa.
“It has never been built before. Even if you go to Uganda, Democratic Republic of Congo [and] Kenya, there is no bridge like this,” he added.
He said it should be named Nyerere Bridge after Tanzania’s first President Julius Nyerere, saying the idea was first mooted by him.
Mr Nyerere led Tanzania, or what was then known as Tanganyika, to independence from the UK in 1960.
He governed the country until his retirement in 1985, and died in 1999.