The croc had been displayed on the banks of the River Aire near Horsforth for years until it was taken by thieves earlier this week.
The 6ft resin model was chained down in the garden of John Brinn's home next to Newlay Bridge, and the criminals are believed to have used bolt cutters to release it.
A crocodile-shaped outline similar to a fossil remains imprinted on the concrete where the distinctive totem was kept.
The Newlay Conservation Society describe the theft as a 'cruel blow' for the area.
The statue has been in place for around a decade, and was originally a gift from John's children.
In a statement posted on the group's Facebook page, the society's members said:
"Residents and visitors to Newlay are upset by the theft of an old friend from a house by the river. The crocodile has been clearly visible from Newlay Bridge for many years and has always been a point of interest for passers-by.
"On Monday night between 10pm and 4am thieves entered the garden of the house next door, bolt cut a locked gate and then bolt cut the steel cable securing the croc in place. Whoever it was who did this planned this meticulously. It's a cruel blow to the owners and to Newlay.
"Please would you keep an eye out for this croc coming up for sale on Ebay, Facebook or other social media sites. Croc is 6ft long and would have required at least two people to lift it and a van to carry it away from the house."
West Yorkshire Police are also investigating the incident.