A labourer walking in the area found a leg belonging to 17-year-old Cara Burke on Sunday, a week after her torso was discovered in a suitcase near a different river.
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Police searching in the same area found her forearms and head.
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Inspector Carlos Raimundo Batista said he was confident the body parts were Cara's.
Police say Mohammed D'Ali Carvalho dos Santos, 20, killed Cara, from Southfields, south-west London, because she threatened to tell his family that he was addicted to cocaine and dealing the drug.
Santos has told police he does not remember most of what happened the night Cara died because he was high on cocaine.