Keepers had hoped the big cats would breed but have been left devastated after Asim, the male they brought in, attacked Melati.
The zoo says their first contact "quickly escalated into a more aggressive interaction" and the seven-year-old male killed the 10-year-old female.
The two tigers had been kept in adjoining enclosures for 10 days so they could get used to one another, but their first interaction 'quickly escalated into a more aggressive interaction'.
After witnessing sufficient evidence and "obvious positive signs", the zoo felt comfortable enough to open the adjoining door and introduce the two predators on Friday morning.
When they finally got Asim away, Melati was dead.
A spokesman for London Zoo said staff were "devastated" and "heartbroken".
As with "all big cats, introductions, however carefully planned, are always considered to be high risk", the zoo said.
Seven-year-old Asim - whose name means "Protector" in Arabic - had been matched with Melati through the European Endangered Species Programme for Sumatran tigers.
"Zoo staff immediately implemented their prepared response, using loud noises, flares and alarms to try and distract the pair, but Asim had already overpowered Melati", the zoo said.
The Sumatran tiger is classified as critically endangered and is on the International Union for Conservation of Nature's red list of threatened animals.
London Zoo describes Sumatran tigers as the "rarest and smallest subspecies of tigers" in the world, and are native to the Indonesian island of Sumatra.
'Asim is a handsome, confident cat who is known for being very affectionate with the ladies in his life - we're hoping he'll be the flawless mate for our lovely Melati'.
Speaking before Asim's arrival, Jo Cook, the coordinator of the EEP program at ZSL, had stressed the importance of the tiger transfers.
ZSL said its Tiger Territory attraction would remain closed for the rest of Friday while its team focused on caring for Asim.