The blue "Please offer me a seat" badge, and accompanying card, were trialled by 1,200 people in September.
It is believed TfL is the first European transport provider to officially recognise hidden conditions in such a way.
Mayor of London Sadiq Khan said the badges "will make a real difference".
There is no set definition of conditions that qualify for the badge and card, but TfL say the system will be based on trust - as with the existing "Baby on board" badge scheme.
The scheme was created, TfL said, in response to comments from its customers who struggled to get a seat because their need was not obvious.
During the trial last year 72% of journeys were said to be easier as a result of the badge, while in 86% of trips participants reported feeling more confident when asking for a seat.
Mr Khan said: "These blue badges will make a real difference to passengers who need a seat but just haven't felt confident enough to ask for one."
James McNaught, who took part in the trial, previously made his own "cancer on board" badge after chemotherapy on his throat left him unable to speak and doses of morphine made him appear drunk.
He said: "This is a brilliant scheme and I am very glad that it is being introduced by the mayor.
"The anxiousness of needing a seat but being unsure whether you will get one can rob people of the confidence to use public transport.
"This simple initiative will make a huge difference to the lives of many people."
Badges for people with hidden health problems have been launched across the Transport for London (TfL) network, following a successful trial.