Police were called shortly before 1pm yesterday (July 28) to the well-known central London street.
The man in his 80s was taken to hospital by the London Ambulance Service.
His condition was initially thought to be life-threatening, but is now thought to be life-changing.
No arrests have been made.
It was reported by MyLondon that the pensioner was hit by bus number 159.
The bus had completed its route and there were no passengers on board at the time of the crash.
A Met Police spokesperson said: “Police called at 12:52hrs following a collision between a bus and a pedestrian.
“The pedestrian, a man in his 80s, was treated at the scene and taken to hospital by the London Ambulance Service.
“He was initially assessed as being in a life-threatening condition, but has now been deemed life-changing.
“No arrests have been made.”
A TfL spokesperson said: “Our thoughts are with the person who has been seriously injured following a bus collision.
“The safety of people travelling in London is paramount and we’re working with the police and operator, Transport UK, to urgently investigate this incident.
“This must have been a distressing incident for everyone involved and we have support available for anyone affected.”
