The former England captain featured in a contact session for the first time and can now play practice matches.
On the mark: Redknapp is happy with Beckham's influence on his team
The move does not mean Beckham is any more likely to play for Tottenham, however.
With LA Galaxy imposing a February 10 deadline on his time at Spurs, Harry Redknapp is not certain that the 35-year-old will even be match fit by then.
Just peachy: Beckham departs Spurs Lodge after another day's training
Redknapp said: 'If they do call him back on February 10 then to do a loan deal now would be a waste of time because by the time David got match fit it would already be February.
'He will be the first to admit that in his first week of training he has felt tired and it's going to be a couple of weeks before he is fit enough.
'He's preparing for a new season in America and this is pre-season for him now. He wouldn't be ready to play in their league at the moment, let alone the Premier League.
'If he could have come until the end of the season, that would have been great. I didn't know it was going to be two months at best.
'But it's been good having him here. Everybody respects him, everybody likes him. There is nothing flash about him. He's not come in here as Billy Big Time, he's joined in everything and he has brought a buzz about the place. You can't teach his desire for the game.'
Meanwhile, Redknapp, who disclosed that Ledley King requires surgery after tearing his groin in training, admitted he is set to fail in his bid to sign Phil Neville. The club also confirmed that a move to the Olympic Stadium in Stratford would not mean a change of the Tottenham name.
Back in action: Bale has recovered from a strain and will face United
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Explore more:People: David Beckham, Harry Redknapp, Phil Neville, Ledley King Places: United Kingdom, America, Olympic Stadium