There have been many references to the Akashic records in major world religions.
In the bible Moses pleads with God on the Israelites behalf after they worship a golden calf, taking responsibility he asks for his name to be stricken out of the book that God has written, as a punishment.
Later in Psalm 139 David tells us that in the same book there is nothing that is not known about him good and bad and even future events.
In David and Revelations it is revealed that this book will be opened for final judgement and those whose names are not in it will not enter heaven.
Edgar Cayse a Christian when asked during an interview stated that the Akashic record and Gods book of life were one and the same.
Q. [What is meant by] The Book of Life?
The record that the individual entity itself writes upon the skein of time and space, through patience - and is opened when self has attuned to the infinite, and may be read by those attuning to that consciousness...
The Book of God's Remembrances?
This is the Book of Life.
The Akashic Records?
Those made by the individual, as just indicated.
Of course the Akashic records have the strongest links to Hinduism, which the name and idea arguably come from.
It is impossible as with many religious ideas to determine where and when it originated but likely goes back far into history.
We do know the Hindu mysticism was taken up by the theosophical movements of the 19th Century.
Organisations such as the Theosophical Society popularised the idea and it survives today in as part of many new age belief systems.