Police made the find while searching the river at about 11am on Sunday, and believe it to be Daniel Berry, although formal identification is yet to take place.
The 42-year-old was reported missing on Sunday, December 20, and officers have since been carrying out searches of the area.
A statement from the charity Vision Homes Association, Mr Berry's workplace, said: "It is with great sadness that we have heard of the death of our colleague Daniel Berry.
"Dan first came to work for Vision Homes Association in November 2016 with no relevant experience or training. He did however, have attributes we look for; enthusiasm, a positive attitude, a sense of fun, but most importantly, a wish to make a positive difference to people’s lives.
"Dan became a much respected, hard-working, valued colleague and friend to his peers; always having a ‘can-do’ attitude. He was universally liked by the people he supported and their families.
"He will be greatly missed by all; and our heartfelt condolences go to his family and loved ones."
A statement from West Mercia Police said: "A body has been recovered from the River Teme and is believed to be Daniel Berry from Ludlow.
"Our thoughts are with his family at this difficult time."