International Business Machines Corp. thinks the technology that underpins the bitcoin digital currency can do a lot more than support cash 2.0. Within the next few months, the venerable tech giant plans to release open source software that could be used to create digital contracts that—like bitcoin transactions—would be recorded publicly and securely on a world-wide computer network.

IBM is zeroing in on a technology called blockchain, which serves as bitcoin’s online ledger. Blockchain allows the bitcoin network to track...