Shackell, 26, who arrived from Wolves in August and will stay with O'Driscoll's side until the New Year, has made eight appearances for Rovers and turned in an impressive display in Saturday's 1-1 draw at rivals Sheffield United.
O'Driscoll said: "He's been terrific ever since he came in. We got him on loan. He's got fantastic attributes about his game.
"He's come in and really adds something to the side. Sometimes loan signings don't work out for you, but Jason has been terrific."
O'Driscoll agreed to sell last season's player of the year Matt Mills in the summer and fellow centre-half Adam Lockwood is sidelined for up to three months after fracturing a bone in his foot last week, so Shackell is expected to form a new partnership with Byron Webster at the heart of defence.