Density functional studies are performed to understand the role of chelating bi-phosphine ligands [(Ph2P(CH2)mPPh2); m=1–4] in modulating the regio-selectivity of benzoic acid addition to 1-hexyne, in presence of ruthenium(II) catalyst [(Ph2P(CH2)mPPh2)Ru(methallyl)2]. The Markovnikov addition to 1-hexyne is observed when catalyst 1a [(Ph2P(CH2)PPh2)Ru(methallyl)2] is employed, whereas a reverse regio-selectivity is witnessed in presence of 1d [(Ph2P(CH2)4PPh2)Ru(methallyl)2]. Anti-Markovnikov addition occurs via the neutral vinylidene intermediates (5a/d) formed after 1,2-hydrogen shift in hexyne coordinated ruthenium(II) complexes 3a/d. The energy profile shows clear preference for Markovnikov addition by 15.0 kcal/mol (𝛥$G^S$L) in case of catalyst system 1a. In contrast, anti-Markovnikov pathway following neutral vinylidenes are more favourable by 9.1 kcal/mol (𝛥$G^S$L) for catalyst system 1d. The Z-enol ester formation is more predominantin the anti-Markovnikov pathway since the activation barrier for this step requires less energy (5.9 kcal/mol, 𝛥$G^S$L) than the one furnishing the E-product. The calculated results are in good agreement with the reported experimental findings.