The man, aged 84 and named only as John, went missing in Bessacarr, Doncaster, on Saturday, sparking fears for his safety as a massive police manhunt was launched.
Details of the location of the discovery have not been released.
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A police spokesman said: “We are sorry to share that a body has been found in the search for John from Doncaster.
"John, 84, was reported missing to us on Saturday.
“Although formal identification has not yet taken place, we do believe the body is that of John and his family has been informed.”
Tributes have poured in following the tragedy.
One person said ‘so sad, thoughts are with the family’, while another wrote ‘poor man, thoughts are with his family at this difficult time’.
Another added: “Rest in peace John. Thoughts are with all at such a tragic time.”
A fourth wrote: “Such sad news. Rip John. My thoughts are with his family.”
Another added: “Love and prayers for you and your family.”
"Heartbreaking , I’m thinking of the gentleman and his family,” read another post.
Another added: “Aww so sad what a lovely lovely guy he was , god bless you John xxx”
A police spokesman said: “We know you have been really concerned and we have seen your comments requesting an update. However, we needed to ensure John's family had been told the news, and that they had had time to talk to extended family and friends before we published anything publicly.”