The Rt Revd Thomas Williams will conduct the service, to be held at 1pm at St Mary's Church in Woolton, in her home city of Liverpool, on Thursday August 20.
The television presenter and former pop star will be laid to rest next to her parents afterwards, according to her family.
Black, 72, died of a stroke after falling and hitting her head at her Spanish villa on August 1. Her husband Bobby Willis died in 1999.
A statement on behalf of her family said: "The funeral of singer and TV star Cilla Black will take place at 1pm on Thursday August 20 at St Mary's Church, Church Road, Woolton in Cilla's home city of Liverpool.
"Cilla's body will then be laid to rest, at a private ceremony, in Allerton Cemetery alongside her parents.
"Her beloved husband, Bobby Willis, was cremated in 1999 and his remains were scattered at her various homes here in the UK and abroad.
"Further details of press arrangements will be released once all the preparations have been finalised.
"Once again the family have asked for their privacy to be continually respected at this difficult time."
Black's body has already been flown back to the UK in advance of the funeral, her publicist said.
The star made a posthumous comeback to the UK music charts last week with her compilation album The Very Best Of.
The greatest hits collection, first released in 1983 and then most recently re-released in 2013, landed its highest ever chart position in 14th spot as fans paid tribute.
It was Black's highest charting album since Sher-oo in 1968, according to the Official Charts Company.
Her former Number One single Anyone Who Had A Heart, first released in 1964, also returned to the charts in 41st place, marking its highest chart position in 51 years.
