Crook revealed she was leaving her position as vice-president for marketing at the coffee brand in October last year, to relocate to the United States with her partner.
In her new role, Crook confirmed she will be based at Netflix's headquarters in Beverly Hills, California, starting in mid-March.
Netflix's content and marketing teams are based in Beverly Hills and the engineers are located in the Bay Area of San Francisco, but Netflix has satelitte offices in European cities including Amsterdam.
It is expected Crook will be required to spend one week a month in Europe overseeing marketing in markets including UK, Netherlands, Denmark, Sweden and Norway.
Her role will focus on the rapid expansion of Netflix throughout Europe into countries including France.
Crook joined Starbucks in October 2012 from Vodafone, reporting to Michelle Gass, president of Starbucks EMEA and relocated to Amsterdam. In her first five months at the coffee retailer, she was responsible for reorganising the EMEA marketing and category team.
Danielle Crook said: "Netflix is an incredibly forward-thinking company with a brilliant culture and I am very much looking forward to joining this company at such an exciting time."