There were scant details of the agreement and no information about participation by each company.
Venezuela's state oil company PDVSA discovered Dragon and neighboring gas fields.
The project marks the first time Venezuela will produce and export gas, Venezuelan vice-president Delcy Rodriguez was quoted as saying in social media posts by PDVSA.
The state-owned oil company said Trinidadian energy minister Stuart Young confirmed NGC and Shell will work hand in hand with the Venezuelan government.
"We have secured the license to the Dragon gas field!" said Trinidad's Prime Minister Keith Rowley in a post on his official Facebook page.
A Shell spokesperson also confirmed the deal, though they said it was subject to final investment decisions: "The Dragon field is located in the Mariscal Sucre region offshore Venezuela, adjacent to the Venezuela-Trinidad maritime border approximately 10 miles (15 kilometers) from Trinidad's Hibiscus platform. The Hibiscus platform is co-owned by NGC and Shell."
The license comes two months after the United States eased sanctions on Venezuela, allowing the OPEC country to export crude and natural gas to its chosen markets. Washington had issued a special license to Trinidad for Dragon and amended it in October to allow Venezuela to receive cash from the gas sales.
Trinidad has been trying to win access to gas from the field to ramp up its exports of LNG and petrochemicals, which have suffered in recent years due to a lack of domestic supply.
Dragon, located in Venezuelan waters near the maritime border between the two countries, was put forth by PDVSA about a decade ago when production tests were made and a gas line partially built. But it was not commercially developed amid lack of partners, investment and, more recently, U.S. sanctions.
Discussions between Shell and PDVSA about pricing formulas applicable to future LNG prices threatened to derail the deal, source close to the talks said.
Trinidad's flagship Atlantic LNG project includes four processing trains that can produce up to 15 million metric tons per annum (MTPA) of liquefied gas. But last year the facility only produced 8.2 MTPA, official figures showed.
Atlantic LNG is a significant contributor to Shell's LNG portfolio. Last year, Shell's share of the facility's output was 4.4 million metric tons or 15% of its global production.
