How do open science practices affect tenure and promotion decisions? Does engaging in open science practices (e.g., reproducibility, data sharing, study preregistration, open access publication) affect tenure and promotion decisions for academic scientists? One can imagine that these would be viewed favorability and scientists would be rewarded for being open. At the same time, however, open science seems to be a movement driven by younger scientists and openness may have no bearing on promotions or even be seen as a distraction from the core production of research. Is there any evidence of the effect of open science on individual career success?
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.