Colin Vasey, 81, was last sighted near Dewsbury Minster at around 6.01am on Sunday, 17 November.
Police divers searching the River Calder discovered his body near to the building yard at Horbury Bridge at around 12.50pm on Tuesday (Dec 17).
Speaking on Tuesday, Detective Chief Inspector Fiona Gaffney, of Kirklees CID, said: “Following an extensive search for over the past four weeks, we are sad to inform the public that a body has been found in the search for Colin Vasey.
“This wasn’t the outcome we were wishing for, but we hope Mr Vasey’s family will now have the closure they need and can begin to grieve for Colin.
"They have requested that their privacy is respected at this time.
“I would like to thank all those who have helped in the search for Mr Vasey – the outpouring of support and the response from the public has been nothing short of immense.
“We have had hundreds of people helping in whatever way they can, from providing and searching for CCTV, to on the ground searches. Their support is greatly appreciated by Mr Vasey’s family, the police and the wider community.”