Sri Lankan navy spokesman Commander Buddhika Sampath said 204 sailors of the IRIS Bushehr were brought to Welisara Naval Base near the capital Colombo.
They underwent border control procedures and medical tests but none were found to have health issues.
About 15 others have been left aboard the ship with Sri Lankan naval personnel for assistance because they had reported a fault with the ship.
The Iranian sailors are interpreting operational instructions, manuals and logs for their Sri Lankan counterparts.
He said the ship will be taken to the port of Trincomalee in eastern Sri Lanka, and remain in Sri Lankan custody until further notice.
The Sri Lankan government took custody of the Bushehr after the US sank an Iranian warship, the IRIS Dena, off Sri Lanka's coast on Wednesday.
The strike marked one of the rare instances since World War II in which a submarine sank a surface warship, and highlighted the expanding scope of the US-Israeli military campaign against Iran.
The Dena had participated in naval exercises hosted by India before heading into international waters on its way home.
At least 74 countries had joined the events, according to India's defence ministry including the US navy which conducted reconnaissance aircraft and maritime patrol drills.
The Indian navy received a distress signal from the Dena but by the time it launched a search and rescue operation, the Sri Lankan navy had already begun its own rescue efforts, the ministry said.
The Sri Lankan navy rescued 32 sailors and recovered 87 bodies.
Iranian Foreign Minister Abbas Araqchi said the Dena had been carrying "almost 130" crew.
The normal crew size for a warship of that class is 140.
Araqchi called the sinking an "atrocity at sea" and said the US would "bitterly regret" the attack.
Sri Lankan President Anura Kumara Dissanayake said late on Thursday that authorities decided to take control of the IRIS Bushehr after discussions with Iranian officials and the ship's captain after one of its engines failed.
"We have to understand that this is not an ordinary situation. It's a request by a ship belonging to one party to enter into our port. We have to consider that according to the international treaties and conventions," he told journalists on Thursday night.
Separately on Friday, he wrote on X: "No civilian should die in wars. Our approach is that every single life is as precious as our own."
The IRIS Bushehr had been described in previous Iranian media reports as a navy logistics ship equipped with a helicopter pad.
Dissanayake said Sri Lanka was guided by neutrality while seeking to uphold humanitarian principles.
"We have followed a very clear stance. We will not be biased to any state nor we will be submissive to any state," he said.
Australia's government confirmed on Friday that three Australians were aboard the submarine that sank the IRIS Dena.
The Australians were there as part of the trilateral US, Australian and UK training program under the AUKUS security pact.
