Officials estimate the new Hopper fare will mean around 30 million journeys previously costing £1.50 will be free every year.
Passengers using the tram network - which serves Croydon and surrounding areas - will also be eligible for the free journeys.
London Mayor Sadiq Khan marked the launch of the Hopper fare by changing buses in Tooting, south-west London, on Monday.
He said: "Today is a landmark day for transport in London, and I'm hugely proud that our new Hopper fare will make bus travel cheaper for millions of Londoners travelling around our city.
"It wasn't right that Londoners had to pay twice simply to change buses, and the Hopper will make 30 million journeys free every year.
"It will make a particular difference to low-income families - many of whom still spend a large proportion of their wages on essential travel costs."
Around 21,000 free journeys were made by 8.30am on Monday, Transport for London (TfL) said.
Passengers using pay as you go with Oyster or contactless payment cards are automatically being charged the lower fare.
Khan said TfL does not yet have the technology to allow unlimited free bus transfers or for passengers who travel on a Tube or train between their two bus trips to be eligible for the Hopper fare.
But he said this will be rectified by 2018.
The mayor told the Press Association: "We're not quite ready yet but what I didn't want to do was wait for everything until 2018.
"We are ready to do the two for (the price of) one, which we started today."
Asked how TfL will afford the revenue lost from the free journeys, Khan replied: "We've found more than that by getting rid of some of the waste, by getting rid of some of the inefficiencies, by bringing in-house, for example, some of the maintenance contracts.
"That means we have more than enough money to pay for the two-for-one, pay for the unlimited bus travel, but also to keep our promise to freeze TfL fares for the entire four years of my first term."
Stephen Locke, chairman of London TravelWatch, said: "Making bus travel more affordable will really help passengers, particularly people on lower incomes with long or complex journeys to work.
"We hope that for many people, the Hopper fare will improve access to jobs in areas they may have previously found it too expensive to get to."