Transport for London (TfL) has said that the Silvertown tunnel, which will link east London to Greenwich, will open on April 7.
Buses for a new Superloop route between Canary Wharf and Grove Park will also start running through the tunnel on the same date.
This, along with other bus routes that use the tunnel, will be free for at least 12 months after the completion of the £2 billion project.
The total number of hourly buses able to cross the river in the area will increase from six to 21.
Charges for drivers will apply from 6am until 10pm, seven days a week.
During peak times – on weekdays from 6am to 10am northbound and from 4pm to 7pm southbound – car and small van drivers will have to pay £4.
This charge is reduced to £2.50 for motorcycles. At off-peak times, all of these vehicles will be charged £1.50.
But drivers will only qualify for the off-peak rate if they sign up to TfL’s auto-pay scheme. If they do not, they will have to pay the higher fee, regardless of when they travel through the tunnels.
Large vans will pay £2.50 off-peak, and £6.50 for peak times. For HGVs, this off-peak charge doubles to £5, increasing to £10 at peak times.
TfL will also introduce the same charges for the existing Blackwall tunnel.
Transport bosses say that both tunnels need to be charged at the same rate as their proximity risks there being worse congestion at any uncharged crossing.
It is expected that journey times will be up to 20 minutes quicker at peak times once the Silvertown tunnel opens.
A new bike shuttle service will also start running to transport cyclists through the 1.4km tunnel.
The service will operate every 12 minutes, seven days a week from 06.30am to 9.30pm.
It will have two stops, one north if the river in Seagull Lane close to Royal Victoria DLR station, and one south of the river in Millennium Way near the junction with Old School Close.