NEW DELHI—India and Saudi Arabia on Wednesday signed an agreement to set up a crude-oil refinery with a capacity to process 1.2 million barrels a day in the western Indian state of Maharashtra.

State-run Saudi Aramco will hold a 50% stake in the refinery while ownership of the remaining half will be shared by three Indian state-run refiners and retailers—Indian Oil Corp Ltd., Hindustan Petroleum Corp Ltd. and Bharat Petroleum Corp Ltd.

Saudi...