Domestically, with Feyenoord failing to break the PSV–Ajax stranglehold on the Eredivisie for the fourth-straight year, and major players such as Henrik Larsson leaving the team, Van Bronckhorst began to search for a new club. He chose to join Dick Advocaat (his former manager at international U-16 and U-18 level) at Rangers, joining the club in 1998 for a reported transfer fee between £5–5.5 million.
Van Bronckhorst was already a regular international when he signed for Rangers in 1998, joining up with compatriot Dick Advocaat, the Scottish club's new manager. In his first competitive game for Rangers, a remarkable UEFA Cup tie away to League of Ireland side Shelbourne (although played at Tranmere Rovers' Prenton Park), Van Bronckhorst marked his debut with a finely-struck goal as Rangers came back from 3–0 down to win the match 5–3. Van Bronckhorst went on to score 22 goals for Rangers (13 in the league, three in the Scottish Cup, one in the Scottish League Cup, three in the UEFA Champions League and two in the UEFA Cup), mostly as a play-making midfielder of notable skill and subtlety, before joining Arsenal for a fee of £8.5 million, signing a five-year contract.