The family also revealed the cause of her death in the statement signed by her sister, Deaconess Toyin Odusote, on behalf of the family.
Oniga, a mother of three, died on Friday at the age of 64 in Lagos.
The late actress, who had been active in the Nigerian movie industry since 1993, hailed from Eku in Agbon Kingdom of Ethiope East Local Government Area of Delta State.
Her sister in the statement dismissed reports that the screen goddess died of the dreaded COVID-19.
According to the family, Oniga died of heart related ailment at a Lagos hospital.
The statement titled, “An Official Statement on the passing of Chief. Rachel Tabuno Oniga”, added that the actress battled the sickness for a short period.
“With a heavy heart and total submission to God, we write to announce the passing unto glory of our beloved sister, mother and grandmother; Chief. Rachel Tabuno Oniga. She died in a Lagos hospital at the age of 64, on Friday, 30th of July 2021, at about 10pm.
“Contrary to diverse reports informing that she died from COVID-19 complications, we write to inform the general public that she died from a heart related issue; an ailment she battled with for a short period before her demise.
“We accept her sudden transition as God’s design and we see it as a function of a race of life well finished. Painful as it may be, we accept it in good faith and total submission to her maker.
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“We therefore desire to be allowed to mourn her death privately for now, as we do this with deep sense of respect for her soul and the glorious life she lived”, the statement added.
It, however, added that burial arrangements for the deceased would be announced soon.
“Burial arrangements will be announced in due cause. We appreciate the calls, messages and condolences expressed by everyone and we pray for a sweet repose of her beautiful soul.
“Please accept this release as the only authentic one on behalf of the family until we come up with another”, it further said.