In this work, we are presenting both lithium and sodium ion capacitors (LIC and NIC) entirely based on electrodes designed from recycled olive pit bio-waste derived carbon materials. On the one hand, olive pits were pyrolized to obtain a low specific surface area semigraphitic hard carbon to be used as the ion intercalation (battery-type) negative electrode. On the other hand, the same hard carbon was chemically activated with KOH to obtain a high specific surface area activated carbon that was further used as the ion-adsorption (capacitor-type) positive electrode. Both electrodes were custom-made to be assembled in a hybrid cell to either build a LIC or NIC in the corresponding Li- and Na-based electrolytes. For comparison purposes, a symmetric EDLC supercapacitor cell using the same activated carbon in 1.5 M Et4NBF4/acetonitrile electrolyte was also built. Both LIC and NIC systems demonstrate remarkable energy and power density enhancement over its EDLC counterpart while showing good cycle life. This breakthrough offers the possibility to easily fabricate versatile hybrid ion capacitors, covering a wide variety of applications where different requirements are demanded.