They have provisionally identified the remains as belonging to 52-year-old Jeremy Sparks who was reported missing in July 2007.
They said clothes and personal items belonging to Mr Sparks were found with the remains near to Middleton Road in Sudbury on 22nd January.
In a tribute, his family said: "Jeremy (Jem) always thought the world of us (his family). He was also like and respected by everyone he met.
"It was distressing for all when he went missing in July 2007 as Jem had kept in regular contact by letters and cards with us all until that time.
"When communication ceased we all became very concerned and carried out extensive local searches and enquiries, but to no avail. With no information or answers we believed Jem to have passed away.
"The current situation is difficult for us all due to the discovery of his remains, but we feel that at last we are moving towards closure.
"We ask that our privacy is respected during this emotional time."
On Monday 27th January a post-mortem examination was carried out and police are treating his death as not suspicious.
Formal identification is yet to take place, but police say it will be done so through dental records.