The crash, just after 06:00 GMT on Wednesday, saw the tram derail as it negotiated a sharp bend in the track.
The 42-year-old tram driver from Beckenham, who was arrested on suspicion of manslaughter, has been released on police bail.
Barbara Dumbleton, a family friend, said Mr Chinnery was "a beautiful lad".
"He always had a smile on his face... he was absolutely lovely," she said.
Tributes also poured in on social media.
One described the Crystal Palace fan as "an amazing happy outgoing person who will always be remembered".
Another read: "Hearts been broken today. Dane is the funniest boy I've ever met in my life. If anyone ever needed anything he'd be there doing all he can to help."
Martin Giles, headteacher at Mr Chinnery's former school Meridian High, said staff and students "have been heartbroken to hear that a former student died".
He said the school believed "at least three other former students have also been injured."
"All of the staff in the school shares their pain at this difficult time," he said.
Tom Dale, who was on the tram when it crashed, said he saw Mr Chinnery as he boarded.
"It was like walking out of a war zone," the 20-year-old chef said.
Mr Dale, who was badly bruised in the crash, said of Mr Chinnery: "He was just a friendly, genuine lad, did no harm to nobody really.
"No-one deserves for this to happen to them."
Crystal Palace issued a statement saying the football club's "prayers are with his [Mr Chinnery's] family and with all the friends and relatives of those victims that have been affected."
It added: "The club wishes a full and speedy recovery to the many people who suffered injuries.
"This was a terrible event in the heart of Croydon and we stand with the community at this difficult time."
British Transport Police (BTP) has not yet officially confirmed the identities of the victims.
Assistant Chief Constable Robin Smith said police would only be able to confirm whether all bodies had been moved from the wreckage "once we've been able to right the carriages".
Officers are investigating claims the tram was exceeding permitted speeds and that the driver may have fallen asleep.
The Rail Accident Investigation Branch (RAIB) said the tram, which had been travelling from New Addington to Wimbledon, derailed as it was negotiating a "sharp, left-hand curve" which has a speed limit of 12mph (20 km/h).
The RAIB said it had been travelling at a "significantly higher speed" than is allowed.
Police expect the crash site to remain sealed off until at least Thursday evening as forensics teams examine the scene.
A BTP investigator said "a number of factors", including whether the driver had fallen asleep or blacked, were being examined as possible causes.
London Ambulance Service said a total of 51 injured casualties taken to two hospitals, with eight having serious or life-threatening injuries.
London Mayor Sadiq Khan, who visited the crash site on Wednesday, warned the number of dead may increase.
Trams are not fitted with any safety protection systems to apply brakes automatically if they are going too fast, according to the Office of Rail and Road.
Some passengers said the tram failed to slow down in its usual place at a bend on the track.
Kevin Snow, 57, from Barnsley, South Yorkshire, said: "Usually as you come out the tunnel you feel the brakes, but I didn't seem to at all.
"I thought 'he should be braking in a minute'," he said. "The next thing I knew we were on our side.
"Everyone was screaming and shouting, a lot of people were injured - lots couldn't move."
Passenger Martin Bamford, 30, from Croydon, said "everyone just literally went flying", adding that people were screaming and there was "blood everywhere".
Speaking outside Croydon University Hospital, where he was treated for fractured or broken ribs, Mr Bamford said: "There was a woman that was on top of me... I don't think she made it at all. She wasn't responsive."
Asked about the driver, he said: "I asked him if he was OK. He said 'yeah'. I said to him 'what happened?' He said he thinks he blacked out."
St George's Hospital in Tooting said three patients "are continuing to be looked after by our surgical and medical teams" after under going surgery.
The hospital said on Wednesday it treated four seriously injured victims and 16 walking wounded.
Clinical director Dr Phil Moss said three had undergone surgery and could be kept in for "several days or even weeks".
Croydon University Hospital's medical director Dr Nnenna Osuji said the derailment had been "distressing" and led to "very challenging circumstances" for hospital staff.
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