The agency cited data from the LSEG, MarineTraffic and Kpler firms.
It identified the tanker as Rich Starry and said it was the first to make it through the strait and to exit the Gulf since the blockade began. The tanker and its owner, Shanghai Xuanrun Shipping Co Ltd, were previously sanctioned by the US for dealing with Iran.
The tanker loaded its cargo at its last port of call in Hamriyah in the UAE.
Reuters also reported that another US-sanctioned tanker, Murlikishan, is heading into the strait today and is expected to load crude oil in Iraq on April 16. The vessel, formerly known as MKA, has transported Russian and Iranian oil, it reported.