Baker replaces acting director, Liz Somerville, who left the AOP in the summer, having covered the position on a temporary basis since 2008, when Ruth Brownlee stepped down to spend more time with her family.
In his new position, Baker will report to AOP co-chairs, Alison Reay, digital & multi-media director at the Telegraph Media Group, and Tim Faircliff, general manager of Consumer Media at Thomson Reuters.
Lee will be responsible for representing the AOP's membership of digital publishers. Prior to Microsoft, Lee was business development director at Lycos UK.
Lee said: "I am excited about joining the AOP at a time when the demand for a strong voice in the industry has never been greater, and the needs of our members never been wider."