The former Preston North End chief executive has worked as part of the Rovers management team for the past 16 years and will take up a seat on the board of directors next month.
Agnew, who has worked in professional football for over two decades, is a lifelong supporter of the Lancashire club.
"This is a time to re-group, look forward and concentrate our efforts only on aspects that we can affect and control," Agnew told the club's official website.
"It is a great honour to be handed this opportunity and I will do all I can to help the club to grow and prosper.
"Suffering relegation last season obviously hurt everyone involved, but we must not get bogged down with what has been and gone."
|16/1||Blackburn are 16/1 with William Hill to win the 2012/13 Championship|
The former Premier League winners ended an 11-year stay in the top flight last term after suffering relegation under Steve Kean following a tumultuous campaign.
Several protests were held throughout the year against owners Venky's but Agnew is hoping to repay the faith they have shown in him.
"The owners are putting their faith in me and I thank them sincerely for that," he said.
"It is now up to me to repay that confidence and to help build a new and bright future for this great football club.
"I am passionate about Blackburn Rovers, my family is steeped in it, and if we can get everyone pulling together for the common good then I believe we can proceed with confidence."