Redknapp brought Keane back to White Hart Lane from Liverpool during last winter's window, but accepts the striker had recently fallen behind Jermain Defoe and Peter Crouch in the pecking order.
With former Chelsea frontman Eidur Gudjohnsen arriving on loan and Russian striker Roman Pavlyuchenko now back in the first-team picture, Redknapp believes the move was best for all concerned.
"It was difficult for him not playing regularly, and he is not happy to have been out of team," said the Spurs boss.
"Crouch and Defoe are in good form, and it can cause you problems when you have too many good players in one position.
"I could not guarantee Robbie that he would start tomorrow in the cup at Leeds, or against Villa at the weekend - and he needs to play.
"Robbie is not happy to sit around taking money without playing - yesterday in training, he worked hard as always, but there was a bit of a 'Mr Angry' to him.
"He has a great enthusiasm for the game, Celtic is his team and it was a move for him I didn't want to stop him doing."
Redknapp, though, maintained: "I cannot see it being permanent. It is only a loan, until the end of the season.
"I would think that might be as far as it goes."
Tottenham may have done a fair bit of wheeling and dealing during the January sales, also bringing back Younes Kaboul, who Redknapp had taken to Portsmouth during the summer of 2008, but the Spurs boss is not impressed by the whole situation, labelled a "circus" by Stoke manager Tony Pulis.
"The window is a bit of a farce," Redknapp said. "It might give excitement for fans, but for managers, I couldn't wait for 5pm to arrive, the phone stops ringing and people stop bothering you with players who are no use to you. I am pleased it has finished again."
Spurs have arranged a friendly against a Dagenham & Redbridge side to give Gudjohnsen and Kaboul a chance to work on their match fitness.
Redknapp, though, admits Spurs will be somewhat down to the bare bones at Elland Road on Wednesday.
"We will probably have three kids on the bench tomorrow, because we have left ourselves short of players," he said. "Ledley King is not fit for tomorrow, but could be available for the weekend.
"Pav has a problem with his groin, it is not 100%. He may have another scan today."
Kilmarnock v Celtic Hat Trick: Keane, R. 14/1