He said their mission was to ensure stability for the UN-backed Government of National Accord (GNA) in Tripoli.
The Libyan government is fighting an insurgency by rebel forces under Gen Khalifa Haftar, based in eastern Libya.
Gen Haftar is backed by Egypt and the UAE, while the UN-backed government is supported by Turkey and its ally Qatar.
Rebel forces have been trying to capture Tripoli and were blamed for an air strike on a military academy on Saturday that killed at least 30 people. They denied any involvement.
The Turkish government has given no details about the scale of the military deployment.
"Our soldiers' duty there is co-ordination. They will develop the operation centre there. Our soldiers are gradually going right now," President Erdogan told the CNN Turk TV channel.
He said Turkey's objective was "not to fight" but "to support the legitimate government and avoid a humanitarian tragedy".
The UN Security Council is expected to meet behind closed doors on Monday to discuss the situation in Libya, AFP news agency reported, citing diplomats.
What do other countries think about the Turkish action?
It has been condemned by several countries, including the US.
Last week, President Donald Trump told Mr Erdogan in a phone call that "foreign interference is complicating the situation in Libya".
Egypt said military intervention in Libya was a "matter of Egyptian national security" and it would defeat efforts seeking "to control" its neighbour, news agency Reuters reports.
While Israel, Greece and Cyprus issued a joint statement warning against the Turkish deployment. They called it a dangerous threat to regional stability, and warned that it breached a UN arms embargo imposed on Libya in order to end years of violence.
Mr Erdogan said Libya's government had requested military assistance.
MPs in Turkey approved the bill allowing the deployment of troops last Thursday with 325 in favour and 184 against.
Libya has been torn by violence since long-time ruler Muammar Gaddafi was deposed and killed in 2011 by Nato-backed forces.
The country has two rival administrations, the UN-backed one based in Tripoli, and Gen Haftar's one in the eastern city of Tobruk.