Former Charlton Athletic player Beale, who took charge of Championship (second-tier) QPR in June, was a part of Rangers' coaching team under their former boss Steven Gerrard and later followed the England great to Aston Villa.
Rangers said in a statement that Beale had signed a contract to 2026.
"Michael is a very exciting appointment for us, and his energy and ambition stood out both when he was here previously, and in the discussions we have had prior to him re-joining," Rangers chairman Douglas Park said.
Beale, who was at the club's training ground on Monday and whose first Premiership fixture will be against Hibernian at Ibrox on Dec. 15, said he was 'hugely proud' to be given the opportunity.
"There are some new faces but some people that I know really well so it is great to see everyone.
"For everyone that works here it is a huge privilege, but to be the manager of this football club, that is extremely special. Some wonderful people have sat in this chair prior to me, and I am hugely proud to be the person sat here now," he added.
Van Bronckhorst, who was sacked last week, replaced Gerrard just over a year ago and guided them to the Europa League final last season, which they lost to Eintracht Frankfurt. He also helped them win the Scottish Cup.
Under the Dutchman, himself a former Rangers player, the club sealed their first Champions League qualification in 12 years but crashed out after the group stage with six losses.
They were the first Scottish side to lose all their group games and returned the worst goal difference of any team in the three decades of Champions League group competition.
Rangers are second in the Scottish top-flight with 33 points from 15 games, nine points behind bitter rivals Celtic with the league having paused for the World Cup in Qatar.
