The contract was awarded by Transport for London which has been consulting Wandsworth council since the previous contractor ceased operating.
In December TfL awarded Complete Pleasure Boats a six-month interim contract to safeguard services.
The new contract allows passengers to pay with Oyster pay as you go and discounts for Travelcard holders and TfL says there will be two thirds more services on weekdays with more stopping points being served.
Wandsworth council and the contractors are funding work to make the route “fully accessible”.
Announcing the new contract, Transport Commissioner Peter Hendy said: “KPMG Thames Clippers bring with them a wealth of knowledge and understanding of operating River Bus services on river Thames, which will benefit the many hundred who will use their services every day.
With improved integration with other River Bus services I am sure more people than ever will make the most of what the river has to offer.”
Wandsworth Council leader Ravi Govindia added: “This news will be warmly welcomed by our residents and commuters who rely on River Bus services to travel around London.
“They will soon be able to access more services every weekday, board and depart at more piers – and experience better integration with the wider transport network across the capital.”
