The Metropolitan Police said the pilot and one other person on the ground died at the scene. Thirteen others were injured – one critically – with six being taken to hospital.
The pilot had requested to divert and land at London Heliport at Battersea due to bad weather after taking off from Redhill Airfield in Surrey.
The rush-hour drama happened in the Vauxhall area and it is believed the pilot was the only person on board.
London fire services sent 22 appliances to the scene as plumes of smoke billowed over a wide area.
It is thought the helicopter may have hit two cars. Video footage shot on a mobile phone showed an entire road blocked by burning wreckage and aviation fuel.
Friends of the crane operator who was supposed to be driving the crane said he was late for work and had he been on time, could have been in the cab when the helicopter struck.
British Prime Minister David Cameron was “very saddened to learn of the fatalities and injuries”, his spokesman said.
Witnesses described seeing the helicopter cartwheeling before it ignited.
Sarah-Beth Casey lives in an apartment near the incident.
She told Sky News: “When I heard the explosion – it was like a little earthquake. It was like a gas explosion. I looked up to see debris falling off the tower.”
Nic Walker said the helicopter crashed on to the street outside his house, setting a car on fire.
He said: “I was awake in bed and heard a helicopter. I was aware of some funny sounds and then a loud engine noise, then a huge bang.
“I pulled on some clothes and ran out to help. There were two people injured on my side of the fire. I think one was a motorcyclist. One seemed to have an eye or brow injury.”
Fire and rescue services were inundated with calls from eyewitnesses as the grey plume of smoke towered into the sky close to Battersea Bridge at around 8am.
The crane was on top of a building called The Tower, in the St George Wharf development.
A spokesman for Berkeley Group, which owns St George, the development company for the building, said in a statement: “We can confirm a helicopter collided with a crane at St George Wharf at 8am this morning. Our thoughts at this time are with the friends and families of those killed in this tragic incident.”
Eyewitness Michael Gavin saw the accident while he was standing at Vauxhall station.
“The top of the crane was actually obscured by fog so I didn't see the impact but I heard a bang and saw the body of the helicopter falling to the ground,” he told BBC News.
The helicopter is understood to be an AgustaWestland 109 (AW109) Power – described by its maker as a “versatile” aircraft used in commercial and military markets.
The light-weight, twin engine helicopter has eight seats and is used for executive transport, offshore and emergency medical services, as well as surveillance and patrol missions for police forces.
Chris Yates, an independent aviation expert, told Sky News: “Helicopters are not supposed to come within 500 feet of any structure such as a high-rise building, so we don't know what caused the pilot to get quite so close.”
After the crash one Twitter user immediately posted a dramatic photograph showing burning wreckage in the road.
The area, roughly ten blocks from the major Waterloo train and Underground station, is extremely congested during the morning rush hour.
Gary Slater, a helicopter expert, told BBC News that flying a helicopter in London is very safe.
“It is monitored by Heathrow radar, which is one of the best in the world,” he said.
But Mr Slater added that today's weather conditions were difficult. “Flying in fog is one of the worst things in a helicopter,” he said.