The Rotterdam club finished second in the Eredivisie this season and dismissed Robin van Persie once the campaign had ended, despite the former striker having a year left on his contract.
Van Persie's first full season in charge yielded a Champions League return, but Feyenoord finished 19 points behind runaway champions PSV Eindhoven, with the club's hierarchy also said to have had concerns over his man-management.
Transfer journalist Fabrizio Romano had reported earlier in the week that Feyenoord were closing in on an agreement with Van Bronckhorst to take over the role, and the club have now confirmed the appointment.
Technical director Devy Rigaux said the return marked a new chapter for the club.
"We want to continue building on our sporting ambitions with a head coach who combines extensive international experience with a deep understanding of the club's culture," he said.
Rigaux added that he had followed Van Bronckhorst's career with great interest.
"He is an outstanding coach and a strong personality," Rigaux said. "His broad experience, combined with his Feyenoord DNA and the hunger for new success that Robert Eenhoorn and I sensed during our conversations with him, give us great confidence that he can help take the club forward again."
Van Bronckhorst spent this past season on Arne Slot's coaching staff at Liverpool, leaving after Arne Slot's own exit from Anfield once the campaign was over.
He has signed a two-year contract at Feyenoord, with the club holding an option to extend it by a further year.
The 51-year-old previously managed Feyenoord between 2015 and 2019, winning the Eredivisie title in the 2016-17 season, and has since had spells at Besiktas and Rangers.
A former Barcelona player during his career, Van Bronckhorst now returns to a Feyenoord side that finished well adrift of champions PSV Eindhoven and will be looking to close that gap immediately.
Sipke Hulshoff, another member of Slot's former Liverpool staff, has joined Van Bronckhorst at Feyenoord as his assistant, having previously worked under him during his first spell at the club.
Rigaux said the partnership between the pair, "further developed and strengthened in England", gave Feyenoord a coaching duo combining international experience with a winning mentality and detailed knowledge of the club.