The Briton will combine Whitmarsh's duties as Group CEO with his existing role of Group chairman and head of the McLaren Automotive sportscar division.
Dennis, who presided over some of the greatest years in the team's history with champions such as Ayrton Senna and Alain Prost, had relinquished his role of Group CEO in 2012 but had increasingly chafed at the team's poor performances on the racetrack.
The team's last championship was with Lewis Hamilton in 2008 and they have not won a constructors' title since 1998.
McLaren endured a dismal season last year, failing to finish on the podium for the first time since 1980. Jenson Button's fourth place in the final race of the season in Brazil was their best result.
The team will be powered by Mercedes this year but will be renewing their partnership with Honda in 2015 and hoping for a return to former glories.
Speculation last month suggested Dennis, who has a 25 percent stake in McLaren, wanted to regain control and replace Whitmarsh as principal.
There has also been speculation that Ross Brawn, the former Honda and Mercedes principal who left the latter team at the end of last year, could be lured to McLaren.
Brawn won the 2009 championship with Button and his own Brawn GP team, which rose from the ashes of Honda after the Japanese manufacturer quit the sport at the end of 2008, that is now Mercedes.
The burly Briton has also been linked to a technical role with the governing FIA.
"I want to clear my mind, take a rest and then decide if I want to return to F1, subject of course to any opportunities existing," Brawn told the BBC last month.
In a 20-minute address to assembled McLaren employees at the Woking factory, followed by a long ovation according to one of those present, Dennis assured them that "there will be change" and also that "we will win again".
Whitmarsh's future was not mentioned in the McLaren statement, and he was not present at the address, but an announcement is expected next month on the future leadership.
"During February I will articulate a new Group strategy and implement the organisational structure best suited to achieving it," said Dennis in the statement.
Sources indicated that there had been no change of shareholdings at McLaren, which is half-owned by Bahrain's investment fund Mumtalakat, and nobody had been sacked or made redundant.
However the statement quoted Dennis as saying the shareholders had mandated him to "write an exciting new chapter in the story of McLaren, beginning by improving our on-track and off-track performance."
He said that over the coming weeks he would be undertaking a "thorough and objective review" of all the McLaren businesses.