The mammal was first spotted in the river around 100 metres from the coastline near Whitstable on Thursday.
It was later seen moving up and down the channel between north Kent and the Isle of Sheppey.
The whale was monitored by the British Divers Marine Life Rescue (BDMLR), which described it as appearing “distressed and confused”.
“We do believe that at times it has been grounded while still being supported in water, when the tide has been at the lowest point over the past couple of days,” the group said on its Facebook page.
“The whale was still swimming but movements were not smooth and it did appear to be distressed and confused, changing directions but not travelling far.
“There was also evidence of slight injury to the animal’s head but nothing significant.”
HM Coastguard and the Marine Police Unit continued to monitor the whale until it was found dead on Saturday morning.
“Unfortunately it had fully stranded and died,” the BDMLR said in an update to its followers on Facebook.
The whale carcass will be recovered for further investigation as part of the Cetacean Stranding Investigation Programme.
While sperm whales are not commonly seen in British waters, around 600 cetaceans - whales, dolphins and porpoises - are found stranded around the UK coastline every year.
Earlier this month a killer whale was found washed up with plastic in its stomach in the Wash, a bay between Lincolnshire and Norfolk.
Three whales were found dead in the River Thames in a two month period last year.
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