Police searched the Clean Plate cafe in Gloucester on the occasion of the disappearance of Mary Bastholm, who disappeared in 1968 at the age of 15.
Serial killer West, who died in prison in 1995 at the age of 53, was previously suspected of her disappearance.
Ms. Bastholm’s body has never been found.
The detective in charge of the investigation said that the search will now take place after “assessments on the scene, to establish whether human remains are present”.
Gloucestershire Police had received possible evidence from a television production company that had made a documentary, suggesting that the body of the missing teenager could be buried there.
This included an image of what appeared to be blue material buried in an area of the cellar. Mary was wearing a blue coat when she disappeared.
Chief Detective Inspector John Turner said: “The analysis of our experts and the material provided by the production company means that there is sufficient evidence to justify the start of the excavation work.
“I spoke to the family and was so impressed with their quiet dignity and gratitude for all the work we have done and will do.
“They understand that we may not find human remains, but they also know that we will do everything possible to determine if Mary is buried there.
“It will be slow and painstaking work, but we have the best people on it and I can reassure our communities that everyone is involved, from my investigative team, our crime scenes, search agents and police liaison officers. families to forensic archaeologists who continue their work are absolutely committed to the work to come. “
In a statement, the teenager’s family said they were happy the police “continue to search for Mary” as it “gives us a chance to put her to rest after all these years.”
He added, “We hope it’s a chance to finally get the fence for Mary. “
Along with his wife Rose, serial killer West has tortured, raped and murdered an unknown number of women over a 20-year period.
Mary’s disappearance in 1968 came at a time when Fred West, who often worked the streets where she worked as a waitress in a cafe, was kidnapping girls in Gloucester.
He allegedly confessed to killing Mary in a conversation with his son, Stephen, but had never admitted her to the police.
Mary’s body was not found during the 1994 excavations of the West House, now known as the ‘House of Horrors’, on Cromwell Street in Gloucester.
West was charged with 12 murders but committed suicide in a Birmingham jail ahead of his trial.
Rose West was convicted of 10 murders in November 1995 and is serving her life.
The officers are expected to be in the cafe for several weeks, the force said.