Kobler will replace Bernardino Leon who brokered a peace deal for Libya that has since run into hurdles over the formation of a unity government, a UN statement said.
Leon is to deliver his last report to the Security Council on Thursday.
The former German ambassador to Iraq and Egypt, Kobler led the UN peace mission in the Democratic Republic of Congo over the past two years and has represented the United Nations in Afghanistan and Iraq.
"The leadership transition will take place in the coming days."
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The 62-year-old former chief of staff to Joschka Fischer, Germany's ex-foreign minister, is stepping in as Libya's political talks appear bogged down in bickering over appointments to plum posts.
In the latest move to address objections over power-sharing, Leon on Monday offered to expand a proposed presidency council from six to nine members, made up of a prime minister, five deputy prime ministers and three senior ministers.
This would ensure more representation from Benghazi, Libya's second city, where protests against the UN deal turned violent late last month, leaving at least 12 dead.
Libya has had two administrations since August 2014, when an Islamist-backed militia alliance overran Tripoli, forcing the internationally recognized government to take refuge in Tobruk, in the east of the country.
The country descended into chaos after the fall of Moamer Kadhafi in 2011.
Leon has chosen Fayez el-Sarraj, a deputy in the Tripoli parliament, to head the government but key players have balked at the choice.
Separately, a announcement was issued from the Emirates Diplomatic Academy, based in Abu Dhabi, on the appointment of Leon as its first director general.