"I call on Libyans to seize this opportunity to promote national reconciliation," he said, a day after the UN-backed unity government announced the end of the battle for the coastal city.
Kobler called for "the integration and rehabilitation of fighters" and the collection of weapons "to give way to a professional security apparatus with a unified command".
He stressed the need for mine clearing to ensure the safe return of displaced people after pro-government fighters expelled IS from the city.
Speaking from the Tunisian capital, the UN envoy called the recapture of Sirte "a major step forward in liberating Libya from terrorism", but warned "Libyans should remain vigilant".
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The fall of Sirte -- 450 kilometres (280 miles) east of Tripoli -- is a major setback for IS, which has also faced a series of military defeats in Syria and Iraq.
IS seized Sirte in June 2015 in the chaos that followed the 2011 uprising that toppled and killed longtime dictator Moamer Kadhafi.
The Tripoli-based Government of National Accord is the centrepiece of Western hopes to stem an upsurge of jihadism in Libya, but it has failed to assert its authority across the country.
A rival authority based in the country's far east has refused to cede power, while its own armed forces led by Marshal Khalifa Haftar have been battling jihadists in second city Benghazi.
Haftar was in Algiers on Sunday, Algerian state media said, where the rival army chief met top officials to discuss "re-establishing stability and security" in Libya.