Tiberi grew up in Frosinone, south of Rome, and came through as a time triallist. He took bronze in the junior time trial at the 2018 European championships, then won the junior world title in the discipline in 2019, riding a spare bike after a crank failed before the first corner. Trek-Segafredo signed him that autumn, though he spent 2020 in the under-23 ranks with Colpack.
His years at Trek passed quietly, with third overall at the Tour de Hongrie in 2021 and a stage win there in 2022. He opened 2023 with eighth overall at the Tour Down Under and seventh at the UAE Tour.
In February 2023 it emerged that he had been fined 4,000 euros in San Marino for shooting and killing a cat with an air rifle the previous June. Trek suspended him for twenty days and terminated his contract in April. Bahrain Victorious signed him from June, and he finished 18th at that year's Vuelta a España.
The following spring he was eighth at the Volta a Catalunya and third overall at the Tour of the Alps, taking the young rider classification there too. At the 2024 Giro d'Italia he finished fifth behind Tadej Pogačar and won the white jersey ahead of Cian Uijtdebroeks and Luke Plapp. He wore the young rider jersey again in the opening week of that year's Vuelta, and won the Tour de Luxembourg outright.
He was third at Tirreno-Adriatico in 2025, 36 seconds off Juan Ayuso and a single second behind Filippo Ganna. The Giro went differently: he came home 17th, with Damiano Caruso the best-placed Bahrain rider in fifth. He took second overall at the Tour de Pologne, 29 seconds behind Brandon McNulty on a race settled by a 12.5 kilometre time trial in Wieliczka, and took the combativity prize on stage 17 of the Vuelta a España.









