DUBAI—Saudi Arabia on Monday for the first time revealed details to investors that show its national oil company is the world’s most profitable business, demonstrating that the cloistered kingdom is willing to undergo unprecedented scrutiny to tap international cash.

With $111 billion in net income in 2018, Saudi Aramco, as the firm is known, had bigger returns last year than Apple Inc. and Exxon Mobil Corp. combined. Before taxes and other expenses, the firm said it made $212 billion, a figure similar to the combined military...