"With great regret, at the request of Time Warner, I have agreed to step down," Albrecht said in a statement issued by Time Warner. "I take this step for the benefit of my Home Box Office colleagues, recognizing that I cannot allow my personal circumstances to distract them from the business."
The announcement -- which brings Albrecht's 22-year HBO career to a close -- came a day after Time Warner said it had given the man behind "The Sopranos" and "Sex and the City" a conditional leave of absence to seek alcohol counseling.
The leave was conditional on "resolution" of misdemeanor charges he assaulted his girlfriend outside the MGM Grand Garden Arena, where the couple had attended an HBO-televised boxing match.
Albrecht was arrested about 3 a.m. Sunday and released after spending the night in jail.
The Los Angeles Times reported Wednesday Albrecht had also allegedly been involved in a physical altercation with a female HBO employee, which HBO paid $400,000 to resolve.
Time Warner appointed HBO Chief Operating Officer Bill Nelson to take over Albrecht's duties on an interim basis. The company would not discuss a permanent successor.