Chevron, with Austrian company OMV taking 20 percent of the two fields, did not disclose how much it was paying Reliance Industries of India in the deal, The New York Times reported Thursday.
There have been about 20 new deposits located in the area in the past five years that contain an estimated 8 billion barrels of oil and gas.
Authorities in Kurdistan are offering companies as much as $5 per barrel, compared with less than $1 offered by the government in Baghdad. It is uncertain, however, how these deals will hold up, considering Baghdad believes it has authority over the region.
Baghdad and Kurdish authorities have been negotiating for years on how the area's oil and gas fields should be handled, but they have yet to reach an accord.
"The political risks are not to be taken lightly. It is going to take time for agreements to be reached," Munton said.
When ExxonMobil made a deal in Kurdistan in 2011, Baghdad barred the company from participating in an auction for exploration rights in one of the country's largest oil fields, West Qurna.