Detective Chief Inspector Paul Waller, who led the investigation, said: "Our thoughts are with the family, especially the boys' father who found them dead when he went to collect them for the weekend after Kara Alexander had failed to return his messages.
Kara Alexander, 47, who denied two counts of murder, was found guilty at Kingston Crown Court on Friday, a court official said.
Samantha Yelland, a senior Crown prosecutor in the CPS London Homicide Unit, said: "Our thoughts remain with Elijah and Marley's family and friends who have been completely devastated by their loss.
The boys' father was due to have them that weekend and became increasingly concerned when he had not heard back from Alexander, the court heard.
He found the boys' bodies together in the lower bunk of their shared bunk bed dressed in pyjamas, the CPS said.
