Mr Miliband told the BBC that Syria had a role to play as a force for stability in the Middle East.
The visit is the latest in a run of exchanges between Syria and European nations aimed at easing tense ties.
It comes a month after Mr Miliband met Syrian Foreign Minister Walid al-Moualem in London for talks.
Building mutual understanding between the UK and Syria was important, Mr Miliband told the BBC.
"Syria has a big potential role to play in stability in the Middle East - it can be a force for stability or it can be a force for instability," he said.
"Over the last 18 months I've been talking with the Syrian foreign minister about her (Syria's) responsibilities in the region, in respect of terrorism, in respect of Iraq, in respect of the Middle East peace process, and we've got the chance now to take those discussions further forward."
Mr Miliband will meet the Syrian president and other top officials on Tuesday morning, before flying on to Lebanon.
Syria has faced diplomatic isolation since the assassination of former Lebanese Prime Minister Rafik Hariri in 2005, even though it denies any role in the killing.
It has also been shunned by the US because of its ties with Iran, the Palestinian group Hamas and the Lebanese Shia political and militant movement Hezbollah.
But European nations, led by French President Nicolas Sarkozy, are now initiating steps to bring Syria back into the international fold, arguing that engagement is the way forward.
On Monday David Milliband visited Israel and the West Bank for talks with top leaders.
He called on both Israelis and Palestinians to maintain the five-month-old ceasefire in Gaza, following recent outbreaks of violence that have triggered an Israeli blockade of the territory.
Photo: British Foreign Secretary David Miliband with Lebanese president Michel Suleiman , during his most recent trip to Lebanon
Tags: Assad, Hezbollah, Iran, Lebanon, source: BBC, Syria, Ya Libnan
