The 21-year old Polish forward has had little luck in gaining a first team spot at DW Stadium but will now get an opportunity with the Rams as manager Nigel Clough believes he can strengthen his squad.
"Tomasz is a talented footballer and someone we have seen on a few occasions whilst taking in games," said Clough.
"We believe he can bring something to the squad and he certainly gives us another option in that attacking area."
Latics boss Roberto Martinez said it was a good chance for Cywka to develop his game further.
"Tomasz is at a crucial point in his career and he needs to be playing first-team football to help reach his potential," he said.
"The deal will hopefully give him that valuable experience in a competitive league, at a top side, and be of great benefit to him."