Sinner entered the tournament ranked 13th in the world ad 11th in the race to the year-end Masters, an eight-player event which in Turin on 14-21 November.
Sunday's final will be the first meeting between Jannik Sinner and Diego Schwartzman.
Brooksby, a 20-year-old from California currently ranked a career-best 70th, reached the final four at an ATP tournament for the third time this season.
Second seed Schwartzman carved out a 6-4, 7-6 (8/6) victory over the three-time Grand Slam title winner who won the last of his 46 career titles in the Belgian port city in 2019.
At 3hr 45min it was the longest best-of-three match this year, the ATP said, eclipsing the 3hr 38min played by Rafael Nadal and Stefanos Tsitsipas in the Barcelona final in April.
Tsitispas, who gave up a two-set lead to lose the Roland Garros final to Novak Djokovic last month, went down 3-6, 6-1, 6-3.
Davis Cup Finals 2019: Andy Murray admits being out of shape after narrowly avoiding loss against Dutch's Tallon Griekspoor
Former World No 1 Andy Murray admitted he was not in the best physical shape to open Britain’s Davis Cup Finals campaign after narrowly avoiding a shock defeat to unheralded Dutchman Tallon Griekspoor on Wednesday.
Tennis Rankings: Rafael Nadal ends year as World No 1 for fifth time in career; Andy Murray jumps to 126 after European Open title
The Spaniard did not make it beyond the group stage of last week's ATP Finals in London but Novak Djokovic's failure to reach the semi-finals meant Nadal closed the year as No 1
Judy Murray hails 'rebirth' of son Andy following first title in Antwerp since hip resurfacing injury
Three-time Grand Slam winner Murray has been selected for Britain's Davis Cup squad after beating Stan Wawrinka to win his first tournament since 2017 at the European Open.
Davis Cup 2019: Andy Murray selected for Great Britain after winning first ATP title in two years at European Open
The group will compete in the new-format Davis Cup in Madrid next month as Murray looks to emulate his star role in Britain's 2015 victory in the competition
European Open: Andy Murray battles past Stanislas Wawrinka in final to clinch first ATP title since 2017
Former world number one Murray, rebuilding his game after career-saving hip surgery earlier this year, fought back from a set and 3-1 down against Wawrinka to claim his 46th career title.
Former world number one Andy Murray reached his first final in more than two and a half years on Saturday and admitted it was a 'big surprise'.
European Open: Andy Murray into first semi-final since 2017 Roland Garros; Jannik Sinner youngest to make it to ATP last four
Former world number one Andy Murray reached his first semi-final since the 2017 French Open with a battling three-set win over Romania's Marius Copil in Antwerp on Friday.
European Open: Comeback man Andy Murray begins campaign with straight-sets win over Kimmer Coppejans
Former world number one Andy Murray began his European Open campaign with a battling 6-4 7-6(4) victory over unseeded Belgian Kimmer Coppejans in Antwerp on Tuesday.
European Open: India's Yuki Bhambri suffers first-round defeat on comeback against Italy's Salvatore Caruso
Yuki Bhambri's comeback to the ATP circuit after recovering from a knee injury didn't go well as he suffered a first-round defeat at the European Open in Antwerp, Belgium.
Indian golfing ace Anirban Lahiri, returning to action after a five-week layoff, added a second successive three under 69 to make the cut at the rain-hit Porsche European Open at Bad Griesbach.