Siew is the running-mate of Ma Ying-jeou, who won a convincing victory in Taiwan's elections in March, and has vowed to improve the island's standing with China once he takes office on 20 May.
Siew attended the conference in his capacity as chairman of the Cross-Strait Common Market Foundation, a non-profit group that works to improve economic co-operation between Taiwan and China.
The two neighbours have had an often tumultuous relationship over the last eight years, when Taiwan was ruled by the pro-independence party.
The country's new leaders intend to mend ties, although they have made clear there are no plans for reunification.
China, however, sees reunification as crucial to achieving its "one China" dream.
Translating the significance of the Hainan meeting into practical improvements will be the next challenge for the two countries.
Powell, left, called the Boao meeting a
'new phase' in China-Taiwan relations [AFP]
Hu has said specifically that talks for direct flights between Taiwan and mainland China should be completed soon.
Such flights along with improved trade links would be a clear indicator that previously icy cross-straits relations are finally thawing.
The Hu-Siew handshake is perhaps a small sign that the two governments will be more willing to work together in the future.
Siew characterised Saturday's encounter as "friendly" and praised Hu for being "pragmatic".
"It not only benefits the peace and stability across the Taiwan Straits but also benefits the peace and security in the Asia," he said.
Hu's comments were more cautious and simply summarised the meeting without reciprocating Siew's praise.
"This occasion inspired us to think deep about cross-straits economic exchanges and co-operation under the new circumstances," Hu said.
The US administration has welcomed the apparent breakthrough, calling it good news for the region.
Attending the Boao conference was Colin Powell, who served as secretary of state in the first Bush administration.
"The two sides have begun down a new path. I think we are at the beginning of a new phase in relations between the parties in Asia," he said.
"So I just wanted to express my congratulations."