Yostin Andres Mosquera, 34, was charged with the murder of two men, identified by police as 62-year-old Albert Alfonso and 71-year-old Paul Longworth.
The two victims had been in a relationship and lived together in a flat in Shepherd's Bush, west London, where Mosquera had also been staying for a short period of time, the Metropolitan Police said.
Remains belonging to the men were also found at the west London flat.
"I know that this awful incident will cause concern not just among residents in Shepherds Bush but in the wider LGBTQ+ community across London," Deputy Assistant Commissioner Andy Valentine said in a statement.
"I hope it will be of some reassurance that whilst inquiries are still ongoing and the investigation is at a relatively early stage, we are not currently looking for anyone else in connection with the two murders."
Police also said evidence gathered so far did not suggest a homophobic motive, but the case has been initially categorised as a hate crime - a classification which will be reviewed as more evidence emerges.
Police in Bristol, southwest England, received reports late on Wednesday of a man with a suitcase acting suspiciously on the Clifton bridge. A second suitcase was later found nearby.
Mosquera, who police said had travelled from London with the suitcases, was arrested on Saturday in Bristol.
He will appear at Wimbledon Magistrates' Court in London later on Monday.
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