Villa are bottom of the table, eight points from safety, with 17 games left.
Hollis told BBC Sport the club needed "shaking up" but insisted that spending money on players was not the solution.
He will work with chief executive Tom Fox, who described the club's current football setup as "broken".
Villa owner Randy Lerner has described Hollis as someone with a "proven track record for getting into the thick of troubled organisations",
Villa's 1-0 home win over Crystal Palace on Tuesday was only their second league win of the season and their first since the opening day, but they are still bottom of the league, eight points behind Swansea, who are one place above the relegation zone.
There is added pressure to stay in the Premier League with clubs set to benefit from the start of a new £5.1bn three-year television rights deal from next season.
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However, West Midlands businessman Hollis, who was appointed on Thursday, said: "If we unfortunately have to go through a relegation phase, we have no fear of that.
"Randy Lerner is committed and is going to support the board and executive team to take the actions we need to put us in the best possible position so we can come up as quickly as possible.
"This club will be here and we will be on a stronger footing."
Fox added: "Where we are this season is not where any of us want to be. Randy feels that very deeply. He knows how difficult it is for the fans facing another relegation battle. It is difficult for the players and everyone in the organisation.
"He is not happy but we do not live in fear of what might happen. The thing that makes Randy feel good about the future of the club is that we are putting these kind of processes in place and he has an executive management team that he trusts.
"He believes in the manager he has got. He is positive right now, despite where we are."
United States-based Lerner, who bought Villa in 2006 and announced at the end of last season he was looking to sell the club, has described Hollis as someone with a "proven track record for getting into the thick of troubled organisations, working with embattled executives and getting results".
"Randy was very clear when I met him that there is some heavy lifting that needs doing at this club to address the structural flaws it has experienced over the last five years," said Hollis. "Randy wanted the work to be done and wanted it done quickly, hence I am here.
"There is a big job to be done. And as chairman I really do want to bring back the confidence to this club, both on the playing side and non-playing side, so we can feel good about what we are doing.
"Time will tell if I am right or not. But I have spent six weeks looking at this and I genuinely believe this needs an overhaul and it needs some solid business principals inputting into it.
"We are going to have to look at how we can shake this club up so we can put it on the correct footing where we can have a position where we can command in the Premier League. That will take some time."
In the early years of Lerner's ownership, Villa established themselves as a top-six Premier League team under the management of Martin O'Neill.
For the last five seasons, though, they have battled against relegation and current boss Remi Garde is their fifth manager in that time.
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"There is something not right with our football set-up at Bodymoor Heath," admitted Fox. "When we talk about it, we say that it is fundamentally broken and has been for a while.
"The results speak for themselves. When a great club like this, with its history and heritage and success it has had in the past, finds itself in a relegation battle for five seasons in a row, despite spending money to bring players in and changing managers, you have to ask yourself 'what is fundamentally wrong?'
"The principles Steve talks about are the ones we need to bring to our football set-up so that when we got to our board and ask them to spend money on acquiring players or coaches, we have a good sense for how that investment is going to pay off for the owner and how it is ultimately going to deliver results on the pitch."
Hollis added: "Randy spent a lot of money last summer and we are not seeing the result of that. This is about hard work, commitment and a focus on continuous improvement."
In the summer, midfielder Fabian Delph and striker Christian Benteke were sold for sizable fees, much of which was reinvested in signing 13 players, many of whom have failed to perform for the club so far this season.
Garde's predecessor, Tim Sherwood, has revealed that the signing of these players was conducted via a "transfer committee" at the club, with Lerner having final say.
But Fox defended the club's recruitment process and said they are looking at ways of improving the squad in January.
"We are taking a deep look at the squad and taking a lot of time with Remi to try and understand what our needs are and the best ways to address those," he said.
"In terms of the process we ran over the summer and will run this January, you can call it what you want - some have called it a committee - but we don't buy or sell players any differently to any other top or successful club.
"If Remi is not happy with a player who has been suggested, he says no. We never end up with a list of players we are targeting that isn't an approved list from the manager."
Aston Villa do not the fear the consequences of relegation from the Premier League and will come back "on a stronger footing" if they do go down, says new chairman Steven Hollis.