The incident took place at Ickenham station, which is served by both the Piccadilly and Metropolitan lines, in west London at 10.30pm on March 28.
After falling onto the track, the passenger was hit by a train before they were discovered by London Underground station staff.
The passenger sustained fatal injuries as a result of the incident.
Today (April 16), the Rail Accident Investigation Branch (RAIB) launched an investigation into the death.
The agency said that it would seek to identify the sequence of events that led to the accident.
The investigation will consider the actions of those involved, the management of staff involved, the arrangements in place to manage the risk of accidents, and any underlying management factors.
Lilli Matson, TfL’s chief health, safety and environment officer, said: “Our thoughts are with the family and friends of the person who sadly died at Ickenham Tube station last month.
“We are supporting the RAIB with its investigation and are conducting our own internal inquiry to understand the causes and any actions that can prevent such tragic incidents in future.
“We undertake a huge range of activity to ensure our network is safe for everyone at all times, and are constantly working to eradicate the risk of such incidents.”