Jimmy Phillips has been in interim charge since Neil Lennon left the club last month, but Bolton's relegation from the Championship was confirmed by Saturday's 4-1 defeat at Derby.
Bolton are now facing life in the third tier of English football for the first time since 1993 after a season of turmoil at the Macron Stadium.
The Trotters faced a winding-up order from HMRC over unpaid taxes, changed ownership and are currently working under a Football League transfer embargo
Bolton have won only four league games all season but Anderson has urged supporters to "stick together" with the club now under the ownership of the Sports Shield group
"It's now time to look forward, not back," Anderson said in a statement on the official Bolton website.
"Whilst this continues to be an extremely challenging and difficult time for us all, it is imperative that we stick together and believe that we will come out the other side a better and stronger football club.
"Bolton Wanderers have a fantastic history and a loyal fan base
We very much have to look to put any past differences behind us, embrace everything that we have going for us and move forward together.
"I understand that words can only mean so much at this moment in time and that we, the new board, will ultimately be judged on our actions.
"We're not shying away from that fact and we accept that there are going to be a lot of difficult decisions to make, both on and off the pitch, as we prepare for life in the third tier."
One of the pressing issues for the new board is to find a new manager and Anderson said over 50 applications for the vacancy have been reduced to single numbers.
"I personally have already had a high level of applicants for the job," said Anderson
"We have had over 50 applications, which shows just in how much high regard our club is held.
"That list has been whittled down to single figures and our process of interviewing the candidates is already well under way.
"We want to hit the ground running next season, which is why we are getting these building blocks in place.
"We want to roll our sleeves up and be positive right from the off, play an attractive style of football and really take the game to our opponents.
"We're working tirelessly to try and get the transfer embargo lifted - that is obviously paramount in our planning.
"We also have a number of key relationships and agreements in place with teams in the top flight with an eye on what we can possibly do in the loan market.
"This is a fresh start for us all
We've been working on this plan for some time - we're now in the process of putting it into action.
"There is a lot of hard work ahead and we have to be on this journey together."
Source : PA
Source: PA