The 48-year-old was last seen at around 3am on Sunday after a night out in the south of Scotland town.
A large-scale search was launched by police and a body was found in the River Nith on Wednesday.
Ms Tyeson’s family thanked police and volunteers who took part in the searches for her.
A statement released by Police Scotland said: “The family of Lynn would like to thank everyone for their concern and messages of support over the past few days following Lynn’s disappearance.
“They would also like to thank all those involved in the search for Lynn, both in the emergency services and all those volunteers who spent time looking for her.”