A British Transport Police (BTP) spokesman confirmed to Reuters that five people had been killed and that the tram's driver had been arrested.
A London Ambulance spokesman said 51 others had been taken to hospital, some with serious injuries.
"A number of people have been taken to hospital with injuries and sadly we can say there has been some loss of life," BTP Assistant Chief Constable Robin Smith said. "It is too early for us to confirm numbers but we are working hard to assess the ongoing incident and are continuing to focus on recovery efforts."
"My thoughts and prayers are with all of those who have been affected by this terrible incident that has taken place on the tram in Croydon," Prime Minister Theresa May said.
Emergency services were called at about 6:10 am (0610 GMT) to reports that a tram had derailed near a stop close to central Croydon, a major transport hub close to south London.
Investigations about the cause of the accident are ongoing.