NOC Chairman Mustafa Sanalla told Reuters by phone from the oilfields on Tuesday that some wells at one of the affected fields, Abu Attifel, had already begun operating and production should resume there by Wednesday.
Abu Attifel is operated by Mellitah, a joint venture between the NOC and Italy's ENI and has been closed since July 2015. Sanalla said he could see gas flares being relit as he was driving to the field with local officials.
"Everybody is happy. We are all celebrating," he said.
Sanalla said the NOC was targeting an increase in national production to one million barrels per day (bpd) by the end of July from 830,000 bpd now. He said Abu Attifel alone should rapidly be able to produce 50,000-60,000 bpd.
Libya's output remains well below the 1.6 million barrels a day it was producing before the 2011 uprising. Armed conflict, political disputes and local blockades have made production levels highly volatile since then.
The dispute with Wintershall had caused a rift between the NOC and the U.N.-backed government in Tripoli. The NOC accused the government of siding with the German company and trying to appropriate powers over oil sector contracts in the process.
The NOC said Wintershall had failed to honour a 2010 memorandum of understanding to convert its concessions to EPSA IV terms, or the standard NOC contract that governs deals with international oil companies in Libya.
Wintershall had said its concession deals with Libya were still valid.
The NOC said in a statement that the agreement announced on Tuesday, "allocates to Wintershall an amount of production sufficient to cover its costs, with all remaining production being allocated to NOC".
"It also provides that during this interim arrangement, the parties will attempt to resolve their dispute regarding the legal framework governing the petroleum operations."
(Additional reporting by Patricia Weiss; editing by David Clarke)