Dudley joined British Prime Minister David Cameron in what was billed as the largest British trade delegation to travel to India.
BP and RIL under the terms of the deal aim to coax 4 trillion cubic feet of natural gas from the KG D6 block off India's east coast.
"We will bring all our expertise in deep water to explore the prolific gas basins in India and BP looks forward to a rewarding and successful exploration program in the coming years," Dudley, BP chief executive officer, said in a statement.
BP stated the proposal is subject to regulatory and government approvals. Once sanctioned, the joint project with RIL would represent more than $5 billion in investments over the next five years.
KG D6 last year produced 2 trillion cubic feet of natural gas and 22 million barrels of oil. BP said more drilling was planned "in the coming months" to see if there are more resources under the offshore field.
BP this week said it was ready to defend itself in a U.S. court over the deep-water oil spill in the Gulf of Mexico in 2010.
2014: The Year in Music [PHOTOS]