Aptamer-based graphene field-effect transistor (GFET) biosensors, known as GFET aptasensors, has gained considerable attention because of their rapidity and accuracy in terms of quantification of a wide range of biomarkers. Development of GFET aptasensors is considered as a cutting-edge technology which can be used early-stage for preventative care and personalized medicine. Biochemical functionalization of graphene channel of GFETs using aptamers, as the biorecognition elements (BREs), is a crucial step in fabrication of GFET aptasensors. This work presents a comprehensive comparison of wellestablished biochemical functionalization approaches applied for the fabrication of sensing films in GFET aptasensors, namely indirect and direct immobilization of BREs. This study is the first of its kind to experimentally compare the two BREs immobilization approaches in terms of their effects on the carrier mobility of the monolayer graphene channel and their suitability for sensing applications. Experimental results confirmed that both approaches can preserve and even improve the carrier mobility of bare graphene channel and hence the sensitivity of the GFET, however, the direct BREs immobilization method was selected to develop an aptameric GFET biosensor as this method enables simpler and more efficient fabrication of the graphene-based aptameric sensing layer. The direct BREs immobilization approach was applied to develop GFET aptasensors for determination of two important protein biomarkers 1) tumor necrosis factor-α (TNF-α) and 2) SARS-CoV-2 spike protein (S protein). The TNF-α GFET aptasensor was able to measure TNF-α in a detection range from 10 pg/ml to 10 ng/ml, representative of its physiological level in human sweat. Moreover, the fabricated S protein GFET aotasensor possessed capability to specifically detect various concentrations of S protein with limit of detection (LOD) down to 500 ag/mL, ranging from 500 ag/mL to 5 ng/mL. Taken together, the proposed sensing platform can be steppingstone for realizing diagnostic tools with applications in point-of-care and point-of-use settings.