Credit scores for decades have been based mostly on borrowers’ payment histories. That is about to change.

Fair Isaac Corp., creator of the widely used FICO credit score, plans to roll out a new scoring system in early 2019 that factors in how consumers manage the cash in their checking, savings and money-market accounts. It is among the biggest shifts for credit reporting and the FICO scoring system, the bedrock of most consumer-lending decisions in the U.S. since the 1990s.

The...