The official said the White House will also name presidential healthcare adviser Nancy-Ann DeParle and White House scheduler Alyssa Mastromonaco as deputy chiefs of staff, The Washington Post reported.
Carney, currently communications director for Vice President Joe Biden, moved to the White House in 2009 after a long career in journalism that included a stint as Washington bureau chief of Time magazine.
Gibbs, who said he expects to leave in mid-February, will be involved in Obama's re-election bid and likely will open a consulting operation to assist in that concern.
Obama inner circle has undergone changes for several months, including the departure of chief of staff Rahm Emmanuel to run for Chicago mayor and economic adviser Larry Summers to return to Harvard University, among other things.
2014: The Year in Music [PHOTOS]