Drivers have faced long delays as the new £1.35bn crossing over the Forth officially opened to traffic.
The first vehicles travelled across the Queensferry Crossing in the early hours.
Motorists faced delays of more than an hour during both the morning and evening rush hours, especially northbound.
Officials believe traffic was heavier than expected because of sightseers wanting to cross the bridge.
The crossing is essentially an extension of the M90 motorway across the Forth with a 70mph speed limit, although operators said an initial 40mph limit will be in place to take account of "driver distraction".
Earlier, the bridge was hit by its first breakdown when a lorry stopped at about 07:00.
Traffic Scotland tweeted: "First breakdown on the @FRC-Queensferry. Mostly on hard shoulder but bum sticking out...slightly!"
The new bridge will take most of the traffic that currently uses the 53-year-old Forth Road Bridge.
The old one will remain open for cyclists, pedestrians and buses.
The Queensferry Crossing will be closed again at the weekend to allow members of the public to walk across it.
About 50,000 people were given tickets after a ballot for a "once-in-a-lifetime" chance to walk over the new bridge on Saturday and Sunday.
There will then be a royal visit from the Queen next Monday, ahead of the bridge fully opening later next week.
On Monday night a collection of vintage, modern and electric vehicles drove on the bridge in a procession to mark the symbolic handover from contractors to the Scottish government.
It was followed by a light show across the bridge to celebrate the completion of the biggest infrastructure project in Scotland in a generation.
First Minister Nicola Sturgeon took part in the procession on Monday night and thanked workers for their efforts.
Economy Secretary Keith Brown said: "It's fantastic. You immediately notice coming over the new bridge - as traffic is now doing - the absence of the slap, slap, slap that you get on the existing bridge.
"It's a very smooth passage right across the Queensferry Crossing. Also, just the excitement of looking at this fantastic new structure from a new angle.
"I think it will be extremely well-received by the people in Scotland who are going to use this bridge."
He added: "It has wind protection, which we couldn't put on the old bridge.
"It will mean this bridge should virtually never have to close because of high winds, which frequently happens on the old bridge.
"So it's a different kind of bridge and it benefits from the advances we have had in engineering. It's a superb addition to the landscape here at the Forth."
The 1.7-mile crossing has a design life of 120 years but could last longer as it has been "designed for maintenance" to ensure it runs smoothly for decades.
To avoid closures the existing bridge has faced in bad weather, wind barriers that can withstand the strongest gusts have been installed along the Queensferry Crossing.
About 1,000 sensors have been fitted to give advanced warning of any problems, allowing maintenance teams to pre-empt potential issues.
Opening the Queensferry Crossing: What now?
Friday 1 September
Early in the morning, the Queensferry Crossing will close again to all traffic.
Police will redirect all vehicles back across the Forth Road Bridge.
It will remain closed until the early hours of Thursday.
Saturday 2 and Sunday 3 September
About 50,000 members of the public, who were given tickets after a ballot, will get a "once in a lifetime" chance to walk over the new bridge on Saturday and Sunday.
Monday 4 September
The Queen will officially open the Queensferry Crossing. She will be joined by the Duke of Edinburgh.
The Moderator of the General Assembly of the Church of Scotland will bless the bridge, and the Queen will cut a ribbon on the south side.
Tuesday 5 September
A chance for a further 10,000 local people and school children to walk the bridge.
Thursday 7 September
The bridge will re-open to traffic, with no pedestrian access.
The initial speed limit will be 40mph but after work has been completed to adapt the Forth Road Bridge public transport will be switched back to the old bridge and the Queensferry Crossing will become a 70mph motorway.
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