The announcement, in a Mercedes statement, had been predicted and ended one of the longest-running sagas of the season while shedding no light on what the 59-year-old had planned for the future.
Mercedes hailed Brawn as the architect of their success and said his duties would be split between Wolff, in charge of business, and Lowe on the technical side.
"The most important consideration in my decision to step down from the role as team principal was to ensure that the timing was right for the team in order to ensure its future success," Brawn said in the statement.
"The succession planning process that we have implemented during this year means we are now ready to conduct the transition from my current responsibilities to a new leadership team composed of Toto and Paddy."
Both hailed the "great leader" on their Twitter feeds.
"Ross has built the foundations for us to succeed in 2014," said Hamilton, who joined from McLaren at the end of last year with Brawn's presence at the team being one of the clinching factors.
"Toto and Paddy are fantastic guys and strong leaders for the team. I've started my training already and can't wait for 2014."
Lowe arrived in June from McLaren, where he had worked with Hamilton, while Austrian Wolff moved from Williams in January to become head of Mercedes motorsport.
Brawn is one of the most successful and respected figures in the sport after winning championships with Benetton, Ferrari and his own Brawn GP outfit.
The bespectacled Englishman, a keen Manchester United football fan, was the tactical brains behind seven-times world champion Michael Schumacher's success at Benetton and Ferrari.
After leaving the Italian team at the end of 2006 to take a sabbatical, and spend some time fishing, he joined the Honda team at the end of 2007 and led them until the Japanese manufacturer withdrew from the sport a year later.
With Brawn, the team that emerged from the remains of Honda, he won both world championships in 2009 before selling to Mercedes.
Brawn said that, with a new V6 turbo engine being introduced in 2014 and significant changes to the regulations, now was the right time to go "to begin a new era of team management".
"The team is uniquely positioned to succeed in 2014 and I am proud to have helped lay the foundations for that success," added the Briton.
"In its different guises over the past six seasons, this team has delivered some of the most memorable moments of my career. Our second place in this season's constructors' championship is an important milestone on the road to championship success," Brawn added.
"I am confident that the future will hold just as much success for the team and will take real pride in having played my own part in those achievements."
Non-executive chairman Niki Lauda thanked Brawn, who has been linked over the past few months to future roles with rival teams as well as the governing FIA run by former Ferrari boss Jean Todt, for his contribution and said Wolff and Lowe were the right men to take the team forward.
"When you consider the step that has been made from finishing fifth in 2012 to the second place that we have secured this season, he has been the architect of this success," the Austrian triple champion said.
"He put the plans in place to recruit key people since early 2011, and the performance this season shows that the team is on the right track.
"We have had long discussions with Ross about how he could continue with the team but it is a basic fact that you cannot hold somebody back when they have chosen to move on. Ross has decided that this is the right time to hand over the reins to Toto and Paddy and we respect his decision."