Khan had pledged a new “Hopper” one hour bus ticket allowing unlimited transfers on buses inside a 60-minute window.
And while the ticket launches today, it will only cover a single change between buses or trams, with the discount applied automatically to Oyster users.
Additionally, customers who travel on trains or tubes between two bus or tram services will also lose out.
Transport for London (TfL) blamed the discrepancy on technical issues, but hopes to roll-out unlimited transfers from next year, when the service will also be expanded to include Tube and train journeys.
Even in its limited early stages, TfL estimates that it will mean 30m bus journeys can now be taken free of charge.
Khan said: “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 30m 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.”
It comes after Khan faced pressure over his plans to freeze all TfL fares over four years, which will not include travelcards used by many Londoners.