Briton Yates effectively secured his second Grand Tour triumph on Saturday when he took the leader's pink jersey with an epic effort in the Italian Alps.
The 32-year-old, who rides for Visma-Lease a bike, is the first man to win the Giro without taking a single stage since Alberto Contador 10 years ago.
Kooij won the bunch sprint which has become a feature of the finales in Rome, pipping Kaden Groves, Matteo Moschetti and Mads Pedersen to claim his second win of this year's hugely entertaining three-week race around Italy.
It was a perfect day for Visma-Lease a bike with Yates and Kooij both victorious in the Eternal City.
Yates started the day stood alongside Pope Leo XIV who blessed the peloton in a short stop in Vatican City before the race proper started.
The riders dismounted in front of the pontiff and Yates shook his hand before standing alongside points jersey winner Pederson, king of the mountains Lorenzo Fortunato and Isaac del Toro for a pre-race blessing.
Del Toro had to content himself with the white jersey for best young rider after failing to spot the danger in Yates' attack on the Colle delle Finestre climb on Saturday which ended up deciding the title.