Jeffries, 30, played for the Bulls in 2008 and 2009, making 46 appearances, before returning to Wakefield, his first English club, at the beginning of 2010.
In a surprise move at the weekend, the Australian signed an 18-month deal to return to Odsal.
Commenting on the move on his blog on the official Bradford website, Platt says that the changed expectations amongst the club’s supporters should help Jeffries settle in second time around.
Platt said: “I am really pleased he is back with us, and I thought he played well when he was here before.
“He got a bit of stick in some quarters but I thought he was one of our better players when he was on the field.
“It was the time when the supporters were still expecting the club to be in the final every year and that was realistically never going to happen and some of the players who came in were blamed somewhat for that.
“He is a quality player and I feel we need another organiser, and he will bring that to the party.”
He made 143 appearances for the Wildcats in his first spell at the club, before moving on to Bradford for the 2008 season.