Griffin has had oversight of the channel since 2006. The promotion gives him responsibility for the day-to-day business at MSNBC.
"I can think of no better person at no better time to fully take the reins at MSNBC than Phil," Capus said in a statement. "The team at MSNBC has accomplished an extraordinary feat in the past 12 months and Phil was the guiding hand in all of it."
MSNBC has steadily built its ratings during the presidential campaigns even as it has weathered criticism for the overt partisanship of election coverage anchors Keith Olbermann and Chris Matthews.
Additionally, Griffin will oversee NBC News' specials coverage. Phil Alongi will remain executive producer of NBC News specials, reporting to Griffin.
Griffin has been at MSNBC since the channel’s launch in July 1996 and with NBC News for more than 25 years. He has produced several of the news division's programs including Nightly News with Tom Brokaw, Hardball with Chris Matthews and Olbermann's first MSNBC show, The Big Show, from 1997-98.