The restructuring process, which comes into immediate effect, also sees general manager Andrew Candy become chief executive while Bristow's son Alan has joined the board of directors.
The move comes with the Gulls currently embroiled in a relegation scrap at the bottom of League Two, out of the bottom two on goal difference with three matches remaining.
In a statement on Torquay's official website, Bristow insists she is happy to be called chairman, but dislikes the title chairperson.
She added: "I was lucky enough to win the lottery nearly 10 years ago and have had more than the allotted 15 minutes of fame as a consequence. I don't enjoy cameras, though end up in photos, since the win anyway, so strive to be fairly elegant.
"For now, if you ask me questions on football, you will get an answer from a passionate fan. Stats were never my thing and it is the simple stat of winning games that we all must concentrate on now.
"Questions about running the club will be answered by a committed learner. My midfield of vice-chairs will keep me in line to start, but I will hopefully catch on quick, and not score too many own goals."
Bristow came to prominence at Plainmoor when her late husband Paul joined a consortium to buy the club in a 2007 after winning £15million on the lottery in 2004, a move that led to Alex Rowe becoming chairman, with Baker then taking over the role in 2009. Baker will now work alongside directors Rowe and Ben Phillips.
A club statement read: "It goes without saying that the immediate priority for Thea and everyone else connected with Torquay United is supporting manager Alan Knill and the players in every way possible, as we fight against relegation.
"Saturday's home game with Barnet is a massive occasion and a massive opportunity to rediscover our form at this crucial stage of the season."