Officers were made aware of the deaths around 11.40pm on Sunday, 26 December 2021, at a property in Raeburn Rigg, in the town.
The couple has been named as Denis and Mary Fell, both aged 73.
The man is due to appear at Livingston Sheriff Court on Wednesday, 29 December 2021.
DCI Kevin Houliston from Police Scotland’s Major Investigation Team said: “Our thoughts are with the family and friends of Mr and Mrs Fell and everyone affected by this tragic incident. A continued presence may be seen in the area as officers continue with their enquiries but this was a contained incident and there was no risk to the wider public.”