In this study, probiotic yeast Saccharomycopsis fibuligera (S. fibuligera) VIT-MN04 was encapsulated with wheat bran fibre (WBF) and exopolysaccharide (EPS) along with 5{\%} polyvinylpyrrolidone (PVP) using electrospinning technique for easy gastrointestinal transit (GIT). The electrospinning materials viz. WBF (10{\%}), EPS (15{\%}), PVP (5{\%}) and electrospinning parameters viz. applied voltage (10 kV) and tip to collector distance (15 cm) were optimised using response surface methodology to produce fine nanofibres to achieve maximum encapsulation efficiency (100{\%}) and GIT tolerance (97{\%}). The probiotic yeast was successfully encapsulated in nanofibre and investigated for potential properties. The survival of encapsulated S. fibuligera VIT-MN04 was increased compared to the free cells during in vitro digestion. In addition, encapsulated yeast cells retained their viability during storage at 4°C for 56 days. The nanofibres were characterised using scanning electron microscopy, atomic force microscopy, X-ray diffraction, thermogravimetric analysis, zeta potential analysis and Fourier transform infrared spectroscopy followed by gas chromatography-mass spectrometry and nuclear magnetic resonance analysis. This work provides an efficient approach for encapsulation of probiotic yeast with the nanofibres which can also broaden the application of the prebiotic like WBF providing an idea for the efficient preparation of functional synbiotic supplements in the food industry.