The show, which was announced last year, is one of several projects being dropped by the streaming giant.
Meghan, a former actress, sued Associated Newspapers for misuse of private information and copyright infringement.
The London High Court had ordered the UK tabloid to print a front-page apology for breaching Markle's privacy.
Meghan Markle said the ruling was a victory not just for me, but for anyone who has ever felt scared to stand up for what’s right.
Meghan Markle has apologized for misleading a British court about the extent of her cooperation with the authors of a sympathetic book about her and Prince Harry.
It is traditional to give royal sons titles reflecting the three historic realms -- England, Scotland and Ireland -- that made up the United Kingdom.