Yostin Andres Mosquera is accused of killing Albert Alfonso, 62, and Paul Longworth, 71, between July 8 and 10.
Their remains were found in two cases dumped at Clifton Suspension Bridge in Bristol last Wednesday.
Further remains were later found at an address in Scotts Road, Shepherd's Bush on Friday.
Mosquera, 34, spoke only to confirm his name, address and date of birth in a short hearing at Wimbledon magistrates' court yesterday.
He was remanded in custody and will appear for a hearing at the Old Bailey tomorrow.
Lead magistrate Christina Ruiz told him: "You are remanded in custody as this court has no powers to consider bail." Mr Longworth was British and Mr Alfonso was originally from France but had obtained British citizenship, according to the Metropolitan Police.
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