“Abrams are already in Ukraine and are preparing to reinforce our brigades,” he wrote in a post on social media.
“I am grateful to our allies for fulfilling the agreements! We are looking for new contracts and expanding the geography of supply.”
Mr Zelenskyy did not say how many Abrams tanks had arrived in Ukraine. The US promised earlier this year that it would send 31 Abrams tanks to Kyiv.
The announcement came shortly after Kyiv announced that a Ukrainian strike on Russia's Black Seat fleet had killed nine people, including two generals.
The attack was reportedly timed to be carried out during a meeting between senior Russian leaders.
Ukrainian attacks have intensified in the Black Sea and Crimea, which was annexed by Russia in 2014.
The arrival of the Abrams tanks also comes as US politicians debate sending more financial assistance to Ukraine.
Mr Zelenskyy visited Washington last week to lobby for continued support.
President Joe Biden's administration has asked Congress to approve $24 billion that would go towards Kyiv's defensive efforts.