The 28-year-old leaves The Valley on a free transfer after making 25 appearances and scoring five goals since he signed from Oldham in July.
Abbott missed Friday night's defeat at Notts County while he was agreeing terms and undergoing a medical.
The former Poland under-21 international is able to make the move as the Polish transfer window does not shut until Monday night.
Addicks manager Chris Powell could dip into the loan market to find a replacement.
However, he still has Bradley Wright-Phillips, Paul Benson, Joe Anyinsah and Liverpool loanee Nathan Eccleston as options in attack.
Source: PA
Source: PA