The boat carrying around 400 migrants was successfully towed to port on Tuesday.
Greek authorities launched a major rescue operation off the coast of Crete for hundreds of suspected migrants.
Passengers on a crowded boat had made a distress call late on Monday, the Greek coast guard said.
The vessel had reportedly lost steering and was drifting in rough seas after setting sail from Libya with 483 people on board, it added.
The migrants -- from Syria, Egypt, Pakistan, and Sudan -- were all transferred to a ferry in southern Crete on Wednesday for temporary housing.
A Greek navy frigate, two Italian fishing vessels, a tanker, and two cargo ships were participating in the initial rescue operation. Strong winds and rough seas had made it impossible to transfer any of the passengers from the stricken vessel, the coast guard said.
But authorities later stated that the boat had been successfully towed to the port of Palaiochora and had docked. There were no immediate reports of any injuries or missing people.
Greek Shipping Minister Giannis Plakiotakis described the rescue effort as the largest in the Mediterranean in recent years.
Seven Egyptian nationals were arrested on Friday on suspicion of sailing the vessel and smuggling migrants to Europe.
According to the preliminary investigation, involving Europol, the passengers had paid a criminal gang between €3,000 and €4,000 each to be transported to Italy.
Tens of thousands of people fleeing conflict and poverty in the Middle East, Asia, and Africa try to make their way into the European Union each year.
Due to increased patrols by the Greek coastguard and EU border agency Frontex, migrant smugglers are now taking a longer and more perilous route south of Crete.
In 2022, more than 1,800 people have gone missing in the Mediterranean on their way to Europe, according to the International Organization for Migration (IOM).
Earlier this month, at least 23 people died when two migrant vessels sank near the Greek islands of Samos and Evia.
The Greek coastguard says it has rescued around 1,500 people in the first eight months of 2022, compared with fewer than 600 last year.
Greek Migration Minister Notis Mitarachi has called on the European Commission to help "fairly" relocate the migrants rescued on Tuesday.
"[Greece] cannot be expected to shoulder an ever-increasing burden out of proportion to their respective capacities," he said in a letter.
“Europe must prove that it is in a position to provide immediate and tangible solidarity,” Mitarachi added.