It comes after Mr Annan secured a pledge by EU countries last week to provide thousands of peacekeepers for an expanded UN force in south Lebanon.
The UN chief's talks are likely to focus on the deployment and role of the 15,000-strong force.
It was authorised to help stabilise the ceasefire between Israel and Hezbollah.
Mr Annan may also be asked to help facilitate a prisoner exchange with Israel demanded by Hezbollah.
Hezbollah chief Sheikh Hassan Nasrallah said on Sunday that "contacts" had begun about a prisoner exchange possibly involving Italy and Lebanese parliamentary speaker Nabih Berri.
Israel however denied any negotiations on a prisoner exchange were under way.
Sheikh Nasrallah also said he would not have ordered the capture of two Israeli soldiers on 12 July which triggered Israel's offensive, had he known it would lead to such a response.
More than 1,100 Lebanese and 159 Israelis died in the 34-day conflict which left much of southern Lebanon in ruins.
Mr Annan will arrive in Beirut on Monday morning for talks with Prime Minister Fuad Siniora, Mr Berri and other politicians.
It is not clear whether he will meet Sheikh Nasrallah, who said he would welcome talks.
Unifil-2, a force of 15,000 soldiers including 7,000 from European Union states to replace the existing small Unifil contingent, is due to be deployed to maintain the fragile ceasefire.
The UN hopes to have some of the troops on the ground within a week, although the EU says it will be two to three months before the whole force is deployed.
Mr Annan has made clear that UN troops will not be asked to disarm Hezbollah by force.
A close aide to Mr Siniora told Reuters news agency on condition of anonymity that the Lebanese government would press the UN secretary-general to pressure Israel to end its blockade of Lebanese airports and harbours.
Mr Annan will find there is plenty of unfinished business, the BBC's Jon Leyne reports from Tyre in southern Lebanon.
Across the south many villages stand utterly destroyed and in some places villagers still feel too insecure to return until Israel completes its withdrawal.
Some public criticism is finally being heard of Hezbollah for triggering the conflict and that is no doubt why the Hezbollah leader has now spoken of a miscalculation, our correspondent says.
His comments, he adds, may also have the perverse effect of reassuring the Israeli government that its actions were successful in their aim of restoring deterrents against such attacks.
After his visit to Lebanon, Mr Annan will also travel to Israel, the Palestinian territories, Syria and Iran.
Reporting from New York, the BBC's Mike Sergeant notes that Mr Annan has not visited Iran since the election of Mahmoud Ahmadinejad as president in 2005.
A previous trip was cancelled after the Iranian leader called for Israel to be "wiped off the map".
But officials at the UN in New York insist that the Iranians need to be "part of the current dialogue" on the Middle East, our correspondent says.
It is understood that Mr Annan will not reach Tehran before Thursday's UN Security Council deadline for Iran to suspend its nuclear enrichment activities, he adds.
In another development, Israeli Foreign Minister Tzipi Livni is to fly to Germany on Monday for talks on Lebanon with Chancellor Angela Merkel in Berlin.
Source:BBCGüncelleme Tarihi: 20 Eylül 2018, 18:16