Per Ramon Antonio Vargas of NOLA.com, Dempsey's family released the news about the 73-year-old, who tested positive for the disease March 25.
Dempsey was living at the Lambeth House retirement community in New Orleans. Per Molly Hennessy-Fiske of the Los Angeles Times, 53 members at Lambeth had tested positive for COVID-19 as of Thursday, and 13 had died.
Dempsey, who was born without toes on his right foot and wore a flat-front shoe for kicking, is best known for his 63-yard field goal to give the Saints a 19-17 win over the Detroit Lions in November 1970. His boot beat the previous league high by six yards.
Dempsey's record was tied (but never broken) thrice before the Denver Broncos' Matt Prater nailed a 64-yarder in 2013.
After his career ended, Dempsey held a few different jobs, including working as a football coach for Archbishop Rummel High School in Metairie, Louisiana.
Dempsey announced in 2012 that he had been diagnosed with dementia. Per Vargas, the final years of his life were spent at Lambeth.
Dempsey is survived by his wife Carlene; his children Toby, Meghan and Ashley; his sister Janice Dempsey; and his grandchildren Dylan, Logan and Quinn.