Moira Anderson vanished aged 11 during a trip to the shops in Coatbridge.
Bus driver and convicted child rapist Alexander Gartshore, who died in 2006, has been linked to her disappearance, which police are treating as murder.
On Thursday, a sheriff granted a request from Moira's relatives to open a grave at the Old Monkland cemetery where they believe she is buried.
Police will now search the family plot of Sinclair Upton, an acquaintance of Gartshore's, in a bid to draw the 55-year mystery to a close.
A spokeswoman for Strathclyde Police said: "Following a court hearing, Strathclyde Police has been instructed to undertake an exhumation of a burial plot within Old Monkland Cemetery.
"A detailed strategy, endorsed by the Crown Office, has been prepared.
"This process is expected to take several days and will involve highly skilled personnel trained in the techniques required for this type of work.
"This is a very sensitive issue and we have been liaising with the families to ensure they are kept informed."
Moira went missing after getting on a bus as she ran an errand to the Co-op for her family.
Her body was never found and Scotland's Lord Advocate Frank Mulholland ordered cold case detectives to reopen the case as a murder earlier this year.
Gartshore's daughter Sandra Brown has written a book detailing her suspicions that her late father was Moira's killer.
Moira's sister Janet Hart, who lives in Australia, launched a petition to get Mr Upton's grave exhumed, believing that Gartshore may have dumped her body there in the days before Mr Upton was laid to rest.
Police are to exhume a family grave in the search for the body of a schoolgirl who disappeared in 1957.