Lebanese troops have crossed the strategic Litani river to take up positions as Israel's army pulls back.
Israeli troops still hold much of southern Lebanon
France has confirmed it is ready to command an expanded international force working along with the Lebanese army, but only under certain conditions.
Israel has already passed control of some of its positions in the south to the current United Nations force there.
It indicated that a full withdrawal from what was a stronghold of Hezbollah could take weeks or even months.
Dozens of Lebanese army trucks, armoured personnel carriers and jeeps are on the move across the Litani using temporary bridges set up to bypass bridges damaged by Israeli shelling.
The vanguard crossed at 0600 local time (0300GMT).
Lebanese Brig Gen Charles Sheikhani said: "Since 1968 the army has not come here. This is our first time since then. We're happy to deploy our army to the south of Lebanon."
About 2,000 Lebanese troops are in the initial deployment, which will rise to the 15,000-strong force approved by the Lebanese Cabinet on Wednesday.
It is a historic step for the Lebanese army and a key element of the UN ceasefire process, the BBC's Nick Childs reports from Beirut.
Lebanese Prime Minister Fouad Siniora said the army deployment was to defend the country and that no weapons would be allowed outside the authority of the Lebanese state.
But precisely what that means for the Hezbollah presence in south Lebanon and its weaponry - whether they merely have to stay out of sight - remains ambiguous, our correspondent says.
An Israeli military spokeswoman said the town of Marjayoun and its surrounding area were now in the hands of troops from Unifil, the 2,000-strong existing UN force.
UN PEACEKEEPING FORCE
Likely contributors: Italy, Turkey, Malaysia, Indonesia
Other possible contributors: Morocco, Spain, Belgium, Finland, Brunei, Germany, Portugal, Pakistan
Current Unifil force: 2,000 troops from China, France, Ghana, India, Ireland, Italy, Poland and Ukraine
Areas close to the border town of Bint Jbeil have also been handed over though the town itself remains under Israeli control, she added.
Bint Jbeil saw heavy fighting with Hezbollah during Israel's month-long war with the militants, sparked by the abduction of two soldiers on the border.
The spokeswoman said the handover would continue gradually over the coming days but it was too early to say how soon Israeli troops would be able to pull out of Lebanon entirely.
Earlier, the chief of staff of the Israeli armed forces said the withdrawal would take seven to 10 days although he also indicated that this would depend on the speed of the expanded UN force's deployment.
French Defence Minister Michele Alliot-Marie has confirmed that France is ready to lead an expanded UN force in Lebanon but only with a clear mandate and sufficient resources.
It seems that these have yet to be finalised, our correspondent says.
Unifil is already under French command and Ms Alliot-Marie confirmed that France would continue to lead it once it grew in strength.
But she refused to be drawn on the number of French troops that would be sent.
"Today, it's not 'How many troops and when?', it's 'To do what and how?'" she said on French TV.
She added that only once a clear mandate had been established would it be clear which other countries would join the larger force.
The UN has been counting on France to provide the backbone of the expanded force and is hoping that at least 3,000 troops could be on the ground within two weeks.
Hard road home
Israeli aircraft have been dropping leaflets warning refugees to stay away from southern Lebanon.
Despite these warnings, there has been a steady stream of displaced people heading home towards their villages.
The UN says around a quarter of a million have already returned but hundreds of thousands are still believed to be on the move.
They face a tough journey with traffic jams and the threat of unexploded bombs, the BBC's Greg Morsbach reports.
A spokeswoman for the charity Oxfam said some 600 roads and bridges had been destroyed.
The UN found 200 cluster bombs near a hospital, in the village of Tebnin.
Many of those who managed to escape days of heavy bombardment are now faced with rebuilding their villages and Hezbollah is offering assistance, our correspondent notes.