Swansea boss Michael Laudrup says it is likely he will bring in a goalkeeper in January as Michel Vorm needs knee surgery.
Manager Jose Mourinho believes Ashley Cole will earn a contract extension at Chelsea.
The club say they have paid a "substantial" undisclosed fee for the 27-year-old, who has been on loan with the Millers since October and scored four goals in 16 appearances.
Frecklington has put pen to paper on a two-and-a-half year deal after the two clubs agreed a fee earlier this week.
The transfer is subject to Football League and FA ratification.