It follows Russian President Vladimir Putin signed treaties on Friday to annex four Ukrainian regions partly occupied by his forces, escalating his seven-month war and taking it into an unpredictable new phase.
The move prompted a flurry of sanctions from western countries, with the US announcing sanctions on hundreds of individuals and companies on Friday.
In a speech announcing the move, translated by the Kyiv Post, Mr Zelensky said: “It is here, in Ukraine, that the values of our Euro-Atlantic community have obtained real vital energy. The strength of the nation that fights for freedom, and the strength of the nations that help in this fight.
“We are de facto allies. This has already been achieved. De facto, we have already completed our path to NATO. De facto, we have already proven interoperability with the Alliance’s standards, they are real for Ukraine – real on the battlefield and in all aspects of our interaction.
“We trust each other, we help each other and we protect each other. This is what the Alliance is. De facto.
“Today, Ukraine is applying to make it de jure. Under a procedure consistent with our significance for the protection of our entire community. Under an accelerated procedure.”
Mr Zelensky was seen signing document flanked by his prime minister and the speaker of parliament in a video posted to Telegram on Friday afternoon.
“Ukraine is ready for dialogue with Russia, but with a different Russian president,” Mr Zelensky said.
Under NATO’s doctrine of collective defence, all countries in the military alliance must come to the aid of one if it is attacked. Were Ukraine to become a NATO power, other nations would be compelled to provide military assistance against Mr Putin’s forces.
Mr Zelensky noted that Finland and Sweden had both begun the process of joining NATO in response to Russian aggression, adding that he understood that the alliance would need to reach a “consensus” on the decision.
He finished his speech saying: “We are completing the dismantling of Russian influence on Ukraine, Europe and the world. Glory to Ukraine!”
Mr Putin has repeatedly blamed NATO and the US for the invasion of Ukraine, without providing any evidence.
Prior to the invasion on February 24, he sought legal guarantees that Ukraine would never be admitted to the military alliance after falsely claiming its eastwards expansion represented an existential threat to Russia.
In other developments, Britain’s Foreign Secretary announced that the UK would step up sanctions against Russia following the “illegal” annexation of four areas of Ukraine.
He said in a statement: “The UK utterly condemns Putin’s announcement of the illegal annexation of Ukrainian territory. We will never recognise the results of these sham referendums or any annexation of Ukrainian territory.
“The Russian regime must be held to account for this abhorrent violation of international law.
“That’s why we are working with our international partners to ramp up the economic pressure through new targeted services bans.”