The 14-year old will be the second youngster to exit Ashton Gate in the space of a week after the Robins lost Kane's team-mate Jacob Maddox to Chelsea.
A host of Premier League clubs were believed to have been chasing Kane's signature but he has opted for a move to Anfield.
Kane has already been tipped for international honours and, similar to Maddox, he had been promoted to City's under-18s team at the age of 14.
He is regarded as one of the best young prospects in the country and has been likened to current Liverpool captain Steven Gerrard in terms of his playing style.
The League One side will be due compensation for Kane's exit.