"Today I express special gratitude to the United States," Zelenskiy said in his evening address, adding that the missiles "have proven themselves".
The US has refused to discuss the delivery publicly but officials familiar with the move also confirmed it earlier on Tuesday.
Fewer than a dozen of the missiles entered Ukraine within the last few days, officials said.
Their arrival at the warfront gives Ukraine a critical ability to strike Russian targets that are farther away, allowing Ukrainian forces to stay safely out of range.
The officials were not authorised to publicly discuss the matter before an official announcement and spoke on Tuesday on the condition of anonymity.
The delivery of the Army Tactical Missile System, known as ATACMS, was shrouded in secrecy, with the expectation that the first public acknowledgment would come when the missiles were used on the battlefield.
That intense secrecy is a marked change from previous US weapons sent by US President Joe Biden's administration.
In nearly all other cases, the US has publicly announced its decision prior to the weapons and equipment being shipped overseas.
Because of lingering US concerns about escalating tensions with Russia, the ATACMS version that went to Ukraine will have a shorter range than the maximum distance the missiles can have.
While some versions of the missiles can go as far as 300km, the ones sent to Ukraine have a shorter range and carry cluster munitions, which, when fired, open in the air, releasing hundreds of bomblets rather than a single warhead.
Cluster munitions are prohibited by more than 100 countries but not by the US, Ukraine or Russia.
According to a US official, the missiles delivered to Ukraine have a maximum range of about 160km.
Ukraine's Special Operations Forces claimed that a night-time attack on targets in eastern and southern Ukraine destroyed nine Russian helicopters and other military equipment and personnel at two airfields in Russia-occupied regions.
The ATACMS would be key in Ukraine's ability to hit the airfield in Berdyansk since it is just within striking distance of the shorter-range version of the missile, and the cluster munitions would be effective in hitting multiple targets.
The closest Ukrainian troop positions on the western bank of the Dnieper River are about 160km from Berdyansk.
Zelenskiy and other Ukrainian leaders had been pressing the US to provide the missiles, which have a longer range than any others provided by the US.
But the Biden administration baulked for months, worried that Ukraine could use the weapons to hit deep into Russian territory, enraging Russia and escalating the conflict.
Biden finally agreed to the delivery last month and told Zelenskiy during a meeting at the White House that the US would finally give Ukraine the ATACMS, according to officials at the time.
The US, however, for weeks refused to provide any details on timing or how many missiles would be delivered although officials suggested that the plan was to send a small number.
Ukrainian forces want to use the missiles to help fuel their counteroffensive as it heads into the muddy and colder winter months, enabling troops to strike behind Russian lines while staying out of firing range.
Sending the cluster munition version will mark the second time Biden's administration has moved to send that type of weapon.
In July, the US agreed to send thousands of cluster bombs to Ukraine.
When used, the bomblets are dispersed over a large area and are intended to wreak destruction on multiple targets at once.
The weapons are banned by many NATO allies because they have a track record for causing many civilian casualties.
Unexploded rounds, which often litter battlefields and populated civilian areas, can cause unintended deaths.
