Delavan is a city in Tazewell County, Illinois, United States. Its population was 1,689 in the 2010 census. It is a part of the Peoria, Illinois Metro…Delavan is a city in Tazewell County, Illinois, United States. Its population was 1,689 in the 2010 census. It is a part of the Peoria, Illinois Metropolitan Statistical Area. Delavan was founded by a group of settlers from Rhode Island. The city derives its name from Edward C. Delavan, a temperance advocate from Albany, New York. A post office has been in operation at Delavan since 1840.