The job of reshaping the world’s most-important gold market has fallen to a pair of little-known startups chosen over industry titans including CME Group Inc., the London Metal Exchange and Intercontinental Exchange Inc.

Boat Services Ltd. and Autilla Inc. are tasked with increasing transparency and modernizing the way $5 trillion of bullion is traded annually in the London gold market. That’s no small feat. Until recently, the system for buying and selling was virtually unchanged for more than a century, with private transactions taking place among a loosely regulated group of banks and dealers.