Augmented-reality company Meta has secured a major vote of confidence from investors, raising $23 million to build holographic headsets that allow people to interact with digital images in the physical world.

The infusion represents the beginning what Meta executives describe as a long and gentle push to replace smartphones and computers with wearable computers. The funding for Meta comes just weeks after Google Inc. made a major change to its high-profile Google Glass initiative and Microsoft Corp. announced its upcoming...