The collision occurred at around 10.20am on Sunday January 29 on Blackness Road in Linlithgow, West Lothian.
The male pedestrian was taken to the Royal Infirmary of Edinburgh but he died on Thursday.
The cyclist did not need medical attention.
Sergeant Dave Waddell said: “Our thoughts are with the family and friends of the man who died.
“Our inquiries are ongoing and we are appealing for anyone who was in the area and who witnessed the crash to get in touch.
“I would also appeal to anyone who was driving in the area and who may have dashcam footage which could assist to contact us.
“We are particularly keen to trace the occupants of two vehicles we believed passed the cyclist just prior to the crash.”