The much-travelled 29-year-old received a hero's welcome as the life-long Bhoys fan arrived at Parkhead just before Monday's midnight transfer deadline in Scotland, and looks set to make his debut against Kilmarnock.
Redknapp brought Keane back to White Hart Lane from Liverpool during February 2009, 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 the 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 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 - on Monday 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."
Source: PA
Source: PA