"I'm delighted the deal has gone through", Iron boss Brian Laws told the club's website. "He's a good young player and we're pleased to have him."
Leeds also included a sell-on clause as part of the deal. Keogh spent three months on loan with Scunthorpe earlier this season and has just completed a one month loan spell with Bury.
Kevin Blackwell sent Keogh his best wishes for the future, saying on the Leeds official website: "I couldn't guarantee Andy first team football at the present time.
"We sat down and had a chat and both parties felt it would be better, certainly in the short term, for the player to get first team experience elsewhere.
"We wish him all the best for the future and hope he enjoys a successful career and we will always keep track of him."
The striker made just one first team appearance for Leeds, coming on as a substitute in the Carling Cup game against Portsmouth at Fratton Park.