I would say you would need a bachelors in graphic design, a diploma/bachelors in UX Design and maybe another in computer science / behavioural science... A masters wouldnt hurt either. Youre looking at more than 8 years of school to apply to a job like that.

After that you might have to intern at their offices, possibly for a while.

Yep, I was right. Heres a job posting for UX:

Qualifications: Minimum 2 to 4 years of UX design experience in a production environment. Bachelor's degree in Interaction Design, HCI, Human Factors, Cognitive Psych, or similar field, or equivalent experience. Superb communication skills. Able to work with other disciplines. Effective at problem solving skills, group brainstorming and problem solving / iterative design. Must have experience working with research. Hands-on experience on at least 1-2 different products (apps, video games, social or location based services). Technical experience prototyping, delivering, and tuning online multi-platform experiences (web, mobile, tablet or PC based). Experience with multiple prototyping, presentation, and documentation methods. Experience working on at least one product with significant online functionality.

https://careers.microsoft.com/jobdetails.aspx?ss=&pg=0&so=&rw=1&jid=139739&jlang=EN&pp=SS

I failed a MS interview because I wasn't excited enough about the product I'd be working on (Edge). Which, fair enough, but I wonder whether they ever found someone qualified who also had a passion for Microsoft Web browsers.