An exothermic reaction involves heat leaving the system in which the reaction is taking place. This measurement of heat quantity is known as enthalpy, and is one of the measurements required to calculate the Gibbs free energy change.
The equation dG=dH-TdS, where dG is Gibbs free energy change, dH is enthalpy change, T is temperature (kelvin), and dS is entropy change (measurement of system disorder), is used to calculate the Gibbs change.
In an exothermic reaction, heat is lost, as said earlier (dH<0), and the entropy usually increases (dS>0, typically large molecules will break apart into smaller molecules, increasing the disorder). Because temperature can never be negative, we have a general system that looks like this:
dG = negative - negative = more negative
so, an exothermic system typically has a dG<0.
