The 19-year-old Pidcock soloed to victory and beat second-placed Johan Jacobs (Lotto Soudal U23) by 30 seconds, with Jens Reynders (WBD Wallonie-Bruxelles development team) finishing in third place more than two minutes behind.
The race was contested over a distance of 170 kilometres, starting in Péronne and finishing at the fabled Roubaix velodrome.
Pidcock was part of a nine-man group before he and Jacobs attacked their companions with 25 kilometres to go. The pair rode together for just a few kilometres when Pidcock decided to take matters into his own hands and launched another attack with still 20 kilometres remaining.
There were no flash celebrations from Pidcock as he crossed the line. Instead, he punched the air with delight. He joins the likes of Bob Jungels, Taylor Phinney, Thor Hushovd and Marc Madiot as a winner of the event.
As well as becoming the first Briton to take the under-23 title, Pidcock is the first to win it having already taken the junior event. Pidcock claimed the junior title in 2017 at the age of 17, also going solo on from far out. On that occasion, Pidcock made his move on the Carrefour de l'Arbre, after bridging across to a breakaway group with 25 kilometres remaining. Pidcock stepped up last year and finished 27th, but appeared in control this time out.
Paris-Roubaix is Pidcock's second road win of the season, after taking a stage of the Le Triptyque des Monts et Chateaux in April. In February he won the under-23 cyclo-cross world title, beating Belgium's Eli Iserbyt.