Passengers will need a prepaid or concessionary ticket, Oyster card or a contactless payment card to travel.
TfL said only 0.7% of all bus journeys were paid for with cash and that tourists were unlikely to be affected.
But the Green Party said more ticket outlets were needed and questioned how vulnerable passengers would cope.
TfL said its research showed the move, which came into force at 04:30 BST, was unlikely to affect tourists "as the vast majority use a prepaid ticket, such as a Visitor Oyster, to get around the capital".
Its drivers have been asked to guide vulnerable people.
Last month TfL introduced the "one more journey" feature for Oyster users, allowing passengers to make one further trip if they have insufficient credit on their card, which TfL said had benefitted around 44,000 customers a day.
Mike Weston, TfL's director of buses, said: "Removing cash from our bus network not only offers customers a quicker and more efficient bus service but it enables us to make savings of £24m a year which will be re-invested to further improve London's transport network."
But Green Party London Assembly member Darren Johnson said questions remained over whether passengers who lost or damaged their Oyster cards would be allowed to travel at all, saying that more than 2,100 Oyster cards were lost, stolen or stopped working on the average day last year.
Mr Johnson said: "I am very concerned that TfL are only planning 19 new Oyster ticket stops in preparation for the cashless switchover. This seems highly inadequate, especially when every ticket office across the tube network is going to be closed.
"I also have serious concerns about the impact which this sweeping change could have on vulnerable passengers."

Csongor Sandor, 30, of Dallow Road, Luton, was arrested in June after police, acting on information, found a photo of the attack on his phone.
Other images of children were also found stored on the device.
At Luton Crown Court he admitted sexually assaulting a child under 13.
Sandor also admitted three counts of making indecent images of children.
The court heard that at the time of his arrest, police found a photo of a young girl being sexually assaulted by Sandor which he had taken three months previously.
The former police officer, from Budapest, had been living in the UK for four years.
The court was told he had been employed at an Amazon depot in Hemel Hempstead and was described as a "man of good character".
Judge Michael Kay QC said although Sandor appeared willing to seek help to tackle his urges concerning children, he posed a risk to the public of committing further serious offences.
He jailed him for eight years and eight months and told Sandor that once he was released he would be made subject to an extended period on licence for five years.
He has also been put on the sex offenders' register.
Cash can no longer be used on any of London's buses in a move that Transport for London (TfL) says will save £24m a year.
[NEXT_CONCEPT]
A former Hungarian policeman living in the UK has been jailed for almost nine years for sexually assaulting a child, in a case a judge said showed "extraordinary levels of perversion".