Six men and one woman died, while 51 others were injured, after a tram derailed.
TfL pledged to do "everything we can to support the families and all those affected".
London's Transport Commissioner Mike Brown said: "The TfL Sarah Hope line is available 24 hours a day to provide advice on a whole range of matters and immediate financial and other support.
"This includes covering funeral costs and travel expenses for relatives."
An initial report into the crash is due to be published by the Rail Accident Investigation Branch (RAIB) later today, though investigators have said it could take "many months" to produce a final report.
Initial indications from the RAIB suggested the tram was travelling at "a significantly higher speed than is permitted". The section at which it derailed had a speed limit of 20 km/h (12 mph).
It is understood that part of the investigation will look to establish whether the 42-year-old driver may have fallen asleep or lost consciousness while in charge of the tram. He was arrested on suspicion of manslaughter and released on bail until May.
Croydon Central MP Gavin Barwell made a statement to the House of Commons on Monday, giving his "profound thanks" to TfL, as well as all the rail professionals, NHS hospitals and others who helped out "in the most difficult circumstances".
Barwell added that while the final report will take months to produce "if urgent safety learning comes to light" during the investigation "that will be published without delay".
"As much as we are all desperate for answers, we need to give the professionals time to do a thorough job. The victims deserve no less," he said.
On Tuesday, Croydon council said two permanent memorials would be created for the victims.