Mr Khan, who oversees TfL, first revealed charges for the Blackwall Tunnel last year, which carries 100,000 cars a day under the Thames and has previously been free.
However, the exact amount for using both Blackwall and Silvertown was only unveiled on Wednesday.
The peak fees will be charged northbound from 6am to 10am and southbound from 4pm to 7pm. Both tunnels will be free to use overnight.
However, a £2.50 discount outside those hours will only be available to people who register their vehicle with TfL’s auto-pay system.
Drivers who fail to pay the right charge face a £180 fine, or £90 if settled within a fortnight.
The tolls could rise in future to keep up with inflation, said Christina Calderato, TfL’s strategy director.
Mr Khan said the Silvertown Tunnel will make journeys up to 20 minutes faster and ease “chronic congestion and pollution”, adding that local low-income drivers will qualify for a 50pc discount from the charges.
TfL said the fees are necessary to manage traffic and pay back construction costs for the new crossing.
It said that because of the tunnels’ proximity in east London, the same levies must be applied to both to avoid a huge pile-up in traffic.
Clean Cities, which campaigns against air pollution, questioned the fairness of the charges given Thames crossings in the west of London are free of charge.
It also said that a decision not to exempt electric vans from the fees will weigh on small businesses.
Oliver Lord, who heads the group, said: “How is it fair that residents and businesses in the east are paying for infrastructure such as this and then those in the west expect a blank cheque to fix Victorian bridges?”
TfL said it will hold an eight-week consultation on the charges.