Russian media quoted the Defense Ministry as saying the convoy of Russian military police had crossed the river at noon (0900 GMT) and "advanced toward the Syrian-Turkish border."
Patrols had begun in the northeast of the city of Manbij and a convoy of Russian troops arrived in the town of Ayn al-Arab (Kobani).
Under the deal, Russia and forces loyal to the regime of Bashar Assad were to move to ensure that the terrorists pull back 30 kilometers (20 miles) from the border as of noon Wednesday.
The deal reached between President Recep Tayyip Erdoğan and Russian President Vladimir Putin allows Turkey to maintain control over areas it liberated this month in northeastern Syria during Operation Peace Spring.
The deal gives the Russian troops and Assad's army control over the rest of the Syria-Turkey frontier.
Ankara and Moscow also agreed to conduct joint patrols in the area 10 kilometers into Syrian territory from Turkey, excluding the city of Qamishli.