Natalia Doherty, 50, a mother-of-three, was last seen in Eastbourne, East Sussex, in April 2003, prompting a murder inquiry.
Police have been searching the garden of a house in Icknield Way, Luton.
Two men, aged 66 and 39, from Luton, have been arrested on suspicion of murder and are in police custody.
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Police said early indications suggested that the remains were those of a female, but no formal identification had taken place.
The older man had previously been arrested on suspicion of assisting an offender and preventing a lawful burial.
'Skeletal remains'
A 71-year-old man from Port Glasgow, Scotland, is on bail on suspicion of the same crimes.
Det Insp Jerry Waite, of the Bedfordshire, Cambridgeshire and Hertfordshire major crime unit, said recent inquiries had led them to the garden.
"Police have been working here since last Monday, where we have been conducting ground survey work and we have discovered the skeletal remains of a person," he said.
"As yet there appears to be no formal identification, but we have informed the family of Natalia Doherty that we believe it could be her and we are supporting them.
"Due to the intelligence we had, we strongly believed Natalia would be here."
Detectives believe that shortly before her death, Ms Doherty travelled to Luton to stay with her late ex-husband, Gerald, at the Regents Arms in Hastings Street.
Det Insp Waite said he wanted to hear from anyone who knew the pair around the time of the last confirmed sighting of Ms Doherty on 15 April 2003.
"We would appeal for them to come forward - especially if they knew them in or around 2003 - and were aware of them being in Luton during February to April 2003," he said.
Human remains have been found in a garden by police investigating the disappearance of a woman who went missing 12 years ago.