The halt in output cut some 500,000 barrels per day or 0.5 percent of global oil supply, in a dispute over various issues. Oil output in the Neutral Zone, which dates back to 1920s treaties establishing regional borders, is divided equally between Saudi Arabia and Kuwait.
Reuters was not immediately able to confirm the reports. Kuwaiti and Saudi officials did not immediately respond to requests for comment.
Al-Qabas said oil industry and government officials representing both countries had met on Thursday and had signed an agreement. Al-Rai said there had been an "historic agreement" without giving details.
Al-Qabas said production would restart in Khafji soon after some administrative procedures and within three months for Wafra.
Khafji is operated by Al-Khafji Joint Operations Co, a joint venture between Kuwait Gulf Oil Company and AGOC, a subsidiary of state oil firm Saudi Aramco. It was shut in October 2014 for environmental reasons and had been producing 280,000 to 300,000 barrels per day (bpd) before its closure.
Wafra has been shut since May 2015 due to operating difficulties. It has an output capacity of about 220,000 bpd of Arabian Heavy crude. US oil major Chevron operates the field on behalf of the Saudi government.