Open Whisper Systems is an independent project, receiving grants and donations through the fiscal sponsorship of the Freedom of the Press Foundation. Last year, the Signal Foundation was created and funded by the aforementioned large donation from Brian Acton, which will take over this role once the IRS approves its 501(c)(3) charitable status.
That money will, minus whatever portion the Freedom of the Press Foundation keeps to cover its overhead, be spent on Signal. And donations for Signal to this foundation are tax-deductible to the extent 501(c)(3) charitable donations usually are.
I have no connection with any of the people, projects, or organizations we've been discussing. But I am the president of another fiscal sponsor 501(c)(3) nonprofit in the free/open source software space, so I'm very familiar with this model.