The bodies of Nothabo Zandile Tshuma, 42, and her daughters Natalie, 15, and five-year-old Nala were found in a house in Great Denham, Bedfordshire, on 6 July.
Ndodana Mkhanyisi Tshuma, who also goes by the name Mark, has now been arrested.
Tshuma, 45, had left the UK two days before their bodies were discovered, according to Bedfordshire Police, and was believed to have gone to Zimbabwe from Heathrow Airport.
He is a British citizen of Zimbabwean heritage, according to the force.
A relative spoke of the family’s “unimaginable loss” in a statement issued by police following their deaths.
They said: “The Khumalo family is deeply saddened to confirm the passing of our beloved Zandile (Nothabo) Khumalo and her two children.
“During this time of unimaginable loss, we wish to express our heartfelt gratitude to everyone who has reached out with prayers, messages of comfort, and support.
“Your kindness and compassion have brought great strength to our family.”
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