Carroll penned a three-and-a-half-year deal to become Swansea's third January signing following the arrivals of Luciano Narsingh and Swedish full back Martin Olsson, whose arrival was made official also on Tuesday.
The 24-year-old had previously played for Swansea on loan from Spurs, during the 2014-15 season. He made 18 appearances and helped the Welsh side reach a record eighth-place finish that year.