The 61-year-old Briton, who won the constructors' and drivers' championships with Brawn GP in 2009 before selling it to Mercedes in 2010, set out his version of events in a book to be published in Britain on Nov. 3.
"What happened at Mercedes is that people were imposed on me who I couldn't trust," he said in 'Total competition, lessons in strategy from Formula One' that he co-authored with former Williams chief executive Adam Parr.
An advance copy has been made available to Reuters.
"I never knew really what they were trying to do. I mean Niki would tell me one thing, then I would hear he was saying something else."
Brawn, the former Benetton and Ferrari strategist who played a big part in Michael Schumacher's seven titles, said Wolff made critical comments in a taped conversation with former F1 team boss Colin Kolles.
"He said that I was resting on my money now. I had got all this money and I wasn't interested in the team any more and I wasn't motivated and I wasn't doing this, I wasn't doing that. That the team needed a fresh impetus," said Brawn.
"So I was beginning to deal with people who I didn't feel I could ultimately trust; people within the team who had let me down already in terms of their approach."
Brawn said he then discovered early in 2013 that Paddy Lowe, now technical head at Mercedes, had been signed from McLaren.
"When I challenged Toto and Niki they both blamed each other," he said. "I met them together to have it out with them and they both pointed to each other."
Neither Wolff nor Lauda were immediately available for comment.
Brawn, 61, said the lack of trust became disconcerting and was not something he was used to.
"Even with Paddy Lowe, I was never quite sure -- he was quite happy to jump in and take my job," he added.
"I couldn't trust those people so I saw no future unless I was willing to go to war and remove them."
Mercedes have won the last three contructors' championships with Lewis Hamilton and Nico Rosberg, both signed while Brawn was in charge, and are on course for a third successive drivers' title.
(Editing by Tony Jimenez)
