Theoretically, these solfege hand signs were originated by John Curwen, however I always heard that Curwen appropriated these signs from Sarah Ann Glover.
Sarah's work, "Scheme for Rendering Psalmody Congregational," discusses many of the shortfalls of traditional notation, like the fact that the difference between a line note and space note could be a half step OR a whole step.
She also invented the concept of pitch ladders. John Curwen loved her ideas, but proposed some changes of which she did NOT approve.
This article, by Celia Waterhouse in the British Kodaly Association, seems to highlight that, while Sarah created our movable do pitch notation, John Curwen did invent the handsigns that we use today.