Guerra was sensationally axed on Tuesday, one year to the day after his appointment as CEO was announced and only seven months after he officially started in the role.
The significant off-field move came with the revitalised Demons flying on the field, boasting a 5-2 record in their first season under new coach Steven King.
The fourth-placed Dees take on top-ranked Sydney in a huge clash at the SCG on Sunday.
Melbourne president Steven Smith issued a brief statement on Tuesday evening confirming Guerra's departure, but did not detail the club's reasons for the decision.
Smith expects to be in a position to confirm a new full-time CEO "shortly".
"On behalf of Melbourne Football Club, I thank Paul for his contribution to the club and wish him all the best for the future," Smith said.
"Brian is a highly respected operator and with over 35 years of experience in AFL clubs he will provide much needed leadership and guidance through this period.
"We are pleased that Brian has agreed to step into the role in an interim capacity until a permanent CEO can commence."
Guerra was integral in Melbourne's decision to appoint King as a replacement for 2021 premiership coach Simon Goodwin, who was sacked last August.
King and Cook have a relationship from their time together at Geelong, culminating in the Cats' drought-breaking 2007 premiership.
Cook played four games for Melbourne in 1977, in a short-lived VFL career.
As CEO, he oversaw West Coast's first two AFL premierships and a further three flags at Geelong, during periods of great success on and off the field for those clubs.
Cook also spent four years as Carlton CEO before handing over to Graham Wright last year, and has been consulting to Melbourne since late last year.
Guerra was boss of the Victorian Chamber of Commerce and Industry when he was appointed as Melbourne CEO last April.
His axing continues a revolving door in the Demons' top offices, with Smith the club's fourth president in the past six years.
While Melbourne are flying on the field, there have been off-field issues, including stumbling blocks in the proposed relocation of the club's headquarters to Caulfield racecourse.
The Demons have also faced competition from Richmond in a battle to secure Waverley Park as an interim base.
Controversy also surrounded premiership defender Steven May's retirement on the eve of the season, when Demons football boss Alan Richardson revealed sensitive personal information in a meeting with players' partners.
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