"Brian has been with the club 10 years and successfully managed the reserve team in the two years we were in the Premier League and won trophies." said Madejski.
"He knows the club intimately, and this is a time for reflection. We're not going to be bumped into anything at all and that's what we're not going to do. We've put things in place and to suddenly change now will be ludicrous. Let's see what unfolds."
McDermott's first game in charge is at Bristol City tomorrow.