The body of Miss Yeates, 25, who had been missing since December 17, was discovered on a snow-covered verge in Longwood Lane, three miles from her flat in the upmarket Clifton area of Bristol.
Although her body had not yet been formally identified, police spoke to her family yesterday. A post-mortem examination is due to take place today.
Chief Superintendent Jon Stratford, of Avon and Somerset Police, said: "Our heartfelt condolences go out to Joanna's family for their loss.
"We have not stopped working hard throughout the Christmas period to find their daughter after she was reported missing.
"Now we will work just as hard to discover exactly what happened to her and how she came to be in Longwood Lane on Christmas morning."
Detectives in Bristol had liaised with North Yorkshire Police officers looking for Claudia Lawrence, the York chef who went missing in March 2009.
Miss Lawrence's father Peter said he was "very sorry" to hear of Miss Yeates's death.
"It is a tragic waste of a young life with everything ahead of her," he added. "The period of waiting for her family and friends, however short or long, feels interminable and they can be assured of my continued prayers and thoughts at this tragic time."