Greaves underwent surgery on an artery in his neck following a mild stroke in February 2012. After a full recovery, he experienced a severe stroke in May 2015 which left him unable to speak. He was placed in intensive care and, according to doctors, was expected to undergo a slow recovery. He was discharged from hospital a month later, his health having "improved considerably" said his friend and agent, Terry Baker. February 2016 saw him recovering slowly from his stroke with the use of a wheelchair after he had been told that he would never walk again. Greaves was announced as a recipient of a MBE in the 2021 New Year Honours list, along with fellow 1966 World Cup squad winner, Ron Flowers, for their services to football. The duo were the last surviving England players from the 1966 Tournament to be honoured by HM the Queen.