Wearing masks and white coveralls, officers escorted migrants camped out on a roadside to the new site in the island’s Kara Tepe.
The notoriously squalid Moria camp burned down last week, leaving more than 12,000 people in need of emergency shelter.
Thursday’s operation included 70 female police officers and no violence was reported.
“As long as it is peaceful, we believe it is a good move,” the head of the UN Refugee Agency’s office in Lesbos, Astrid Castelein, said.
“Here on the street it is a risk for security, for public health, and it’s not dignity, which we need for everyone.”
Authorities said the fires were set deliberately by a small group of inhabitants angered by Covid-19 lockdown restrictions.
Six Afghans, including two minors, have been arrested on suspicion of arson.
Most of the migrants made homeless set up makeshift shelters made of sheets, blankets, reeds and cardboard along a stretch of road near the gutted camp.
The new site consists of large family tents erected in an old army shooting range by the sea.
By late Wednesday night it had a capacity of around 8,000 people, according to the UNHCR, but only around 1,100 mostly vulnerable people had entered.
New arrivals are tested for the coronavirus, registered and assigned a tent.
“This is an operation for the protection of public health and with a clear humanitarian mission,” the police said in a statement.
It said 450 people had been moved to Kara Tepe on Thursday morning and 250 of them had already entered the new camp after undergoing a rapid test for the coronavirus.
The rest were waiting to enter, while more people were due to arrive.
The medical aid organisation Doctors Without Borders said Greek police were preventing its staff on the island from accessing a clinic it has set up there.
Moria had a capacity of just over 2,700 people but more than 12,500 people had been living in and around it when it burned down.
The camp and its squalid conditions were held up by critics as a symbol of Europe’s failed migration policies.
The European Union is due to issue proposals to overhaul the bloc’s migration policy next week in an effort to end years of division among member states.
As a frontier state, Greece is pressing for increased participation by other EU members in relocation schemes – unpopular with many central and eastern European countries – but has also suggested alternative obligations may be assigned to countries wishing to opt out of relocation.
Speaking at a debate in the European Parliament on the situation in Greece, EU Commissioner for Home Affairs Ylva Johansson said “there can be no more Morias” and it is time for a fresh start on migration.
Several EU members have offered to take in refugees from Greece, led by Germany.
It says it will take in 1,553 refugees from Greek island camps who have had their asylum applications approved.
