The former Rangers manager takes up the role under fellow Dutchman Arne Slot.
He led Rangers to the 2022 Europa League final and had a brief spell at Besiktas before becoming a UEFA match analyst.
A Liverpool statement said: "Former Netherlands international and captain Giovanni van Bronckhorst joins the Premier League champions in the position of assistant coach, subject to receiving a visa.
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"Van Bronckhorst won a host of major honours during a playing career that included spells with Feyenoord, Glasgow Rangers, Arsenal and Barcelona, and since retiring as a player in 2010 after reaching the World Cup final that year with his country, he has moved into the dugout, starting out in an assistant role at Feyenoord.
"He advanced to take charge of the Eredivisie club himself from 2015 to 2019, and his time at the helm of Feyenoord featured a Dutch league title in 2016-17 and two KNVB Beker successes.
"Van Bronckhorst subsequently took the reins at Guangzhou R&F in China, then Rangers – who he led to a Scottish Cup victory and the Europa League final in 2021-22 – and most recently Besiktas, departing the Turkish outfit in late 2024."