Reuters saw buses leave the steelworks, where defenders had held out in a complex of bunkers and tunnels, in a convoy escorted by Russian armoured vehicles.
Five arrived in the Russian-held town of Novoazovsk, where Russia said the wounded would be treated.
What will happen to the fighters was unclear.
The Kremlin said Russian President Vladimir Putin had personally guaranteed the prisoners would be treated according to international standards.
But a Reuters witness said seven buses carrying Ukrainian fighters from the Azovstal garrison arrived at a former penal colony in the Russian-controlled town of Olenivka near Donetsk.
TASS news agency said a Russian committee planned to question the soldiers, many of them members of the Azov Battalion, as part of an investigation into what Russia calls "Ukrainian regime crimes".
The denouement of a battle which came to symbolise Ukrainian resistance took place as Russia's invading forces struggled elsewhere, with troops retreating from the outskirts of Kharkiv in the northeast.
Ukraine's negotiator Mykhailo Podolyak said on local television on Tuesday that progress could not be made in peace talks if Russia did not recognise the situation on the ground.
Russia invaded Ukraine on February 24, saying it wanted to "denazify" the country, to the bewilderment of the international community.
"To this day, they live in a world where there is supposedly a Ukrainian Nazism," Podolyak said, adding there was only "Russian Nazism".
A ceasefire could be discussed only after a complete withdrawal of Russian troops, he said, with only a complete liberation of all occupied territories acceptable.
Russia earlier confirmed the end of talks.
"No, negotiations will not continue. Ukraine has practically left the negotiation process," Russian Deputy Foreign Minister Andrei Rudenko told reporters.
On the international front, Swedish Prime Minister Magdalena Andersson said Sweden and Finland will on Wednesday hand in their respective applications to join NATO, abandoning their long-standing policy of neutrality over concerns about Putin's wider intentions.
The leaders expressed optimism they could overcome Turkey's objections to them joining amid a flurry of diplomatic activity aimed at smoothing their path into the 30-member military alliance.
The complete capture of Mariupol is Russia's biggest victory since its invasion and gives its forces total control of the Sea of Azov coast and an unbroken stretch of eastern and southern Ukraine.
But the port city now lies in ruins, and Ukraine believes tens of thousands of people were killed under months of Russian bombardment and siege.
Russia said at least 256 Ukrainian fighters had "laid down their arms and surrendered" including 51 severely wounded.
Ukraine said 264 soldiers, including 53 wounded, had left.
Russian defence ministry video showed fighters leaving the plant, some carried on stretchers, others with hands up to be searched by Russian troops.
While both sides spoke of a deal under which all Ukrainian troops would abandon the huge steelworks, many details were not yet public, including how many fighters still remained inside and whether any form of prisoner swap had been agreed.
Ukraine's Deputy Defence Minister Hanna Malyar told a briefing that officials in Kyiv would not disclose how many fighters were inside the plant until all were safe.
"The 'Mariupol' garrison has fulfilled its combat mission," the General Staff of Ukraine's Armed Forces said in a statement.
"The supreme military command ordered the commanders of the units stationed at Azovstal to save the lives of the personnel."
In a statement on Monday, the Azov Regiment, the main Ukrainian unit that had held out in the steelworks, said it had achieved its objective over 82 days of resistance by making it possible to defend the rest of the country.
The regiment, now part of Ukraine's territorial defence forces, originated as an ultra-nationalist militia, and Russia has portrayed defeating its fighters as central to its stated objective of "de-Nazifying" Ukraine.
Russia blames them for mistreating Russian speakers, one of its war justifications, which Ukraine and its backers call a bogus pretext.
with reporting from DPA
