The bodies of a man and a woman were recovered from Breydon Water, Great Yarmouth, on Thursday.
The couple were in their early 60s and from the local area, officers said.
The deaths were initially treated as unexplained but police said they were now satisfied there are no suspicious circumstances.
More news from Norfolk
Emergency services were called to the area shortly after 11:20 BST when a member of the public reported seeing the bodies on a mudbank.
Norfolk Police said they were still trying to trace the couple's next of kin.
The deaths of two people whose bodies were spotted on a tidal mudbank in Norfolk are not being treated as suspicious, police have said.