"Paul is looking forward to staying at the club and playing his part in the fight for Premiership survival."
Earlier today The Whites said that Robinson would be joining Spurs for a fee in excess of £2m, which would have seen the player remain at Elland Road until the end of the season.
Rumour has it that with Leeds having two loan Premiership players already (Jermaine Pennant and Caldwell), Robinson could not be sold and loaned back to them, as it would make three, which would be against the rules.
Robinson, who has four England caps, is regarded as the long-term England goalkeeper and Spurs were keen to sign him as their only experienced keeper is 34-year-old American Kasey Keller.
Leeds also confirmed that striker Bridges would join Newcastle United on loan until the end of the season, with Scottish international defender Caldwell moving the other way.