UN leader Ban Ki-moon also said he was stepping up efforts to convene a Syria peace conference, sending special envoy Lakhdar Brahimi to the region for talks with key governments.
Kaag, a UN assistant secretary general who speaks fluent Arabic and has wide Middle East experience, will head a joint UN-Organisation for the Prohibition of Chemical Weapons mission to destroy poison arms belonging to Damascus.
The UN Security Council has set a deadline of mid-2014 for the mission, but experts say the approximately 100-strong team to be assembled faces an uphill struggle in the conflict-stricken country.
But, with about 1,000 tonnes of chemicals to be eradicated, no disarmament mission of this scope has ever been carried out in the midst of a war.
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"We have no illusions on the challenges ahead," Ban said alongside Kaag.
"The situation in Syria remains dangerous and unpredictable. The cooperation of all parties in Syria is required."
The UN says well over 100,000 people have been killed in Syria since protests against President Bashar al-Assad in March 2011 turned into an anti-regime uprising.
"I am deeply honored and I am mostly humbled to be trusted with this very complex and challenging assignment," Kaag told reporters without commenting on the situation in Syria.
Ban also said he was increasing efforts at "all levels" to hold a Syria peace conference in Geneva in mid-November.
He said UN-Arab League Syria envoy Brahimi would go to the Middle East for talks with "key parties" and that UN political chief Jeffrey Feltman was in Moscow for talks.
Another envoy would go to Turkey to meet representatives of the divided opposition, he added.
Some Syrian opposition groups have said they would refuse to take part in a Syrian National Coalition delegation as long as Assad remained in power.
"We are calling on all who truly wish to work for peace and a new democratic Syria to focus not on military actions but rather on ensuring the success of this conference," Ban said.
The OPCW said earlier that its inspectors have checked 11 out of 20 sites identified by the government as chemical weapons facilities.
The chemical arms watchdog -- which was awarded the Nobel Peace Prize last week -- and Western governments are carrying out separate research into whether all facilities have been declared.