Bournemouth will pay £6m for the left-back who has played 11 times for the Reds, having come through the ranks at Anfield.
Smith is an Australia international and has won seven caps for his country. However, despite being born in Australia and being a full senior international for the Socceroos, Smith represented England at U-17, U-19 and U-21 level.
The 22-year-old was on Liverpool's USA tour but flew home to discuss a deal with Bournemouth.
The defender will become the second player to make the move from Anfield to Bournemouth this summer following Jordon Ibe's move to the Cherries.