Both clubs will go head-to-head in the semi-final as they bid to win promotion to the Premier League.
Brook, who last week confirmed his retirement from boxing, fought Errol Spence Jr at Bramall Lane in 2017 while his former Ingle Gym stablemate Wood is hoping for a big night at the City Ground after successfully defending his WBA world featherweight title against Michael Conlan in March.
“I’m backing them one-hundred per cent,” Brook said of Sheffield United’s chances.
"We have been to the play-offs many times and come up short, let’s hope we get this one.”
The first leg will be played at Bramall Lane on Saturday with the return fixture at the City Ground next Tuesday.
Brook added: "Obviously he will be there, we will be in touch with each other when they are playing – he will be saying his team’s going to win and vice versa.”
"He’s had a brilliant back end of his career, he’s done great things. I have a lot of love for Leigh Wood.”
The Blades have a dismal play-off record and have been beaten in all of their previous eight attempts at promotion via the end-of-season contest.
They did overcome Forest in the First Division play-off semi-final in 2003, however, and head into the first leg on the back of three straight wins.
Both of the club’s league meetings this term ended in a 1-1 draw.
Steve Cooper’s side finished the regular season with a draw after missing out on automatic promotion.