Hammersmith and Fulham Council said its “radical plans” would see the bridge potentially reopen for pedestrians and cyclists next summer, and motor vehicles two months later.
The 134-year-old west London bridge has been closed to traffic since April 2019 when cracks appeared in its pedestals.
It then closed to pedestrian, cyclist and river traffic in August after a heatwave caused the faults to “significantly increase”.
The council said “early assessments” indicate motorists would pay an average of £3 to drive across the bridge.
It claimed its plan would help reduce restoration costs to “around £100 million” and allow traffic to use it from the middle of 2022.
The bridge would have a “double-decker” structure, with an upper level carrying cars and buses, while pedestrians and cyclists would use the lower level, the council said.
A technical study conducted jointly by architects Foster + Partners and specialist bridge engineers COWI found it is “feasible” using the existing bridge foundations.
The full restoration would be completed in 2023.
The Labour-run council also said ownership of the Grade II* listed bridge could be transferred to a charitable trust.
Council leader Stephen Cowan said: “Hammersmith Bridge is one of the oldest suspension bridges in the world and the most expensive in Britain to repair.
“While we’re working to fully restore the bridge as quickly as possible, we’re also determined to put in place the necessary governance and long-term funding arrangements that will make sure it is properly maintained well into the next century.
“We are proposing a twin-track solution which reunites maintenance funding with transport use and puts the bridge into a charitable trust.”
Roger Ridsdill Smith, head of structural engineering at Foster + Partners, said: “The feasibility study supports the technical viability of the proposed temporary crossing, showing that it has the potential to be significantly cheaper than a scheme that repairs the bridge in situ.
“It also offers the possibility of the bridge reopening earlier than previously envisaged.”
The plans will be discussed next week at the Hammersmith Bridge Taskforce meeting.