Caulker is moving to the Swans on a season-long loan.
The 19-year-old has impressed in previous loan spells at Yeovil and Bristol City and will strengthen the Swans' defence following their promotion to the Barclays Premier League.
The England Under-21 international will put pen to paper within the next week on a deal which will be reviewed in January.
City chairman Huw Jenkins told the club's official website: "We are delighted to have agreed terms with Tottenham regarding a deal for Steven.
"The deal has been very close for the last couple of weeks. I met (Tottenham chairman) Daniel Levy at a Premier League meeting in Darlington and spoke at length about Steven.
"We feel his general size and ability are perfect qualities to add to our team. Steven is a young, upcoming player that is a big talent, and he is looking forward to being part of our squad in the Premier League.
"It is an exciting signing for us. There was other interest in him prior to this deal being agreed, but Tottenham felt it was perfect for Steven to continue his deal here."