The 18ft (5m) northern bottle-nosed whale was placed in a special pontoon in shallow water near Battersea Bridge.
It was then tethered close to two boats and towed to a barge which is heading for the river estuary.
Experts hoped it could be let out into deep waters but the plan now is to release it off Whitstable in Kent.
If the whale is too weak experts may take the decision to put it down.
Tony Woodley from the British Divers Marine Life Rescue (BDMLR), which is leading the rescue operation, said the vet on the barge was "pessimistic" about the whale's chances.
Rescuers tried to keep the whale cool as they moved it by barge
The vet had told him the animal was suffering muscle stiffening and was under stress due to what it has gone through and being out of the water.
"The plan was to go round at least to the English Channel before it was released, but now it is just get as far out of the Thames as possible," he said.
"We have the awful trade off of how far out we can take it and how long we can keep it out of the water."
A BDMLR spokesman said the barge should reach the a location known as "Shivering Sands" 15 miles off the coast of Whitstable from 2100 GMT to 2130 GMT.
A sighting of the whale on Saturday morning near Albert Bridge, in Chelsea, disappointed rescuers buoyed by an earlier report that it had been seen in Greenwich, which is closer to open water.
But as the rescuers moved the whale applause broke out among the 3,000 onlookers some on Battersea Bridge, which had been closed, as the whale passed beneath.
It is on an inflatable raft which is functioning as "makeshift whale mattress" on which it is being constantly watered down and monitored by experts.
The whale was captured near Battersea Bridge
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It has been given several injections including antibiotics and earlier a vet on board the barge said the whale's had sustained cuts and its breathing was irregular.
Mark Stevens, from BDMLR, said lifting the animal onto the barge had "gone like clockwork" but it was the "scariest thing I've ever done in rescuing whales".
The whale, which could weigh about four tonnes, was first spotted at 0830 GMT on Friday by a man on a train and has since attracted massive public and media attention.
It soon became clear there was cause for concern, as the animal came within yards of the banks, almost beaching, and crashed into an empty boat, causing itself slight bleeding.
There were reports of a pod of whales in the Thames estuary earlier in the week, and it was possible that the whale had become separated from this group.
There was also an unconfirmed sighting of a whale in Southend in Essex on Friday.
It was the first sighting of the endangered species in the Thames since records began nearly a century ago.
In an unrelated incident, what is thought to be a harbour porpoise was found dead on the banks of the Thames in Putney, south-west London, on Saturday afternoon.
Battersea Bridge
Crowds watch the rescue
Battersea Bridge watching the whale

Rescue teams are attempting to save the life of the whale which has been swimming in the London Thames river over the past few days. The northern bottle-nosed whale, which had gotten weaker and weaker, became beached this afternoon. Rescue teams quickly moved the whale onto an inflatable pontoon, keeping the whale in water but with its blowhole above the surface.

Experts then tried to evaluate the condition of the whale by performing ultrasound checks to see how much blubber and blood the whale has, and by taking some blood tests. The breathing rate of the whale was around four inhalations per minute.

The pontoon is currently being towed by a barge slowly downstream.

The British Divers Marine Life Rescue team lead the rescue effort. They hope to be able to release the whale in as deep water as possible, but only if it is in good enough health. If the whale is considered to be in too weak a condition to survive, it may be euthanised, experts have said.

The rescue mission is being filmed by television crews, including from helicopters, and broadcast live onto rolling news channels. Mark Stevens, a member of the British Divers Marine Life Rescue team reported on the situation live on TV using a mobile phone, direct from the scene where he was standing in the water. At one point he asked the BBC to tell their helicopter to fly higher, as the noise made the whale's breathing rate temporarily go up.

The whale sightings have captivated the British public, with spectators lining the banks of the Thames to take photographs and try and spot the whale. However, the inital surprise at seeing the whale soon turned to concern as experts fear for the whale's long term health. Initial plans to transfer the whale from the barge "Crossness" to a deep-sea ship have been abandoned as the condition of the whale deteriorates, but it is still hoped to release the whale in the Thames estuary.