The incident happened around 6.20pm on Tuesday, 25 January on the A803 Main Street in Linlithgow Bridge.
The 81-year-old woman was taken to the Royal Infirmary of Edinburgh after she was struck by a black Volkswagen Transporter van but died a short time later.
A 54-year-old female who was driving the van was uninjured.
Police are appealing for information following the incident.
Sergeant Scott Kirkpatrick of the Road Policing Unit in Livingston said: “Our thoughts are with the woman’s family and friends at this difficult time.
“We are carrying out enquiries to establish the full circumstances and would urge anyone with information which could help to get in touch.
“We would also be keen to speak to anyone who may have dashcam footage from the area on Tuesday evening.
“Anyone who can help is asked to call 101, quoting reference 2701 of 25 January.”