How do open science practices affect tenure and promotion decisions?
Based on my limited experience, I am not confident that open science practices affect tenure decisions directly, at least at the moment. However, there are many indirect benefits.


Making the paper publicly available increases the citations. See this article by Kurtz et al. from 2005. This blog post provides a nice summary and critique of this literature. 
Making the data publicly available increases the citations. See this article by Piwowar, Day, and Fridsma from 2007. This blog post provides a nice overview.
I am confident based on my own experience that a reproducible workflow is a much more efficient workflow (e.g., much easier to pick up and make progress after an invitation to revise and resubmit). Efficiency should then lead to higher quality output, higher quantity output, or both. And both quality and quantity contribute positively to tenure and promotion. Further, one important step in encouraging other researchers to use your data is allowing them to easily reproduce the original findings. This step is automatic for reproducible research.
I'm less optimistic about the incentives for pre-registration (at least in my field of political science). In my view, there are still strong incentives to not pre-register studies. The culture is changing, but somewhat slowly. Here's is a blog post discussing some of these pros and cons.


Indeed, this article from 2013 by Ebrahim et al. titled "Effective Strategies for Increasing Citation Frequency" lists many practices that are also open science practices, such as self-archiving papers, publishing in open-access journals, placing papers in open-access repositories, and making the data publicly available.