Police said the two victims had previously been in a relationship but still lived together in west London, adding that the suspect had been staying with them.
Evidence in the investigation so far had not pointed to a homophobic motive but it had been classified as a hate crime.
Police named the victims as Albert Alfonso, 62 years, a British citizen originally from France, and Paul Longworth, 71 years.
It was learnt that officers launched a manhunt after the suitcases were discovered on Clifton Suspension Bridge in Bristol, southwest England last week. More human remains were later found at a flat in London as Mosquera will appear before magistrates in the capital later on Monday.
Clifton Suspension Bridge, designed by the pioneering engineer Isambard Kingdom Brunel, is one of the oldest surviving suspension bridges in the world. Opened in 1864, the bridge over the Avon Gorge is one of Bristol’s top tourist attractions and a city symbol.