Alzheimer’s disease (AD) has been associated with the hallmark features of cholinergic dysfunction, amyloid beta (Aβ) aggregation and impaired synaptic transmission, which makes the associated proteins, such as β-site amyloid precursor protein cleaving enzyme 1 (BACE I), acetylcholine esterase (AChE) and synapsin I, II and III, major targets for therapeutic intervention. The present study investigated the therapeutic potential of three major phytochemicals of Rosmarinus officinalis, ursolic acid (UA), rosmarinic acid (RA) and carnosic acid (CA), based on their binding affinity with AD-associated proteins. Detailed docking studies were conducted using AutoDock vina followed by molecular dynamic (MD) simulations using Amber 20. The docking analysis of the selected molecules showed the binding energies of their interaction with the target proteins, while MD simulations comprising root mean square deviation (RMSD), root mean square fluctuation (RMSF) and molecular mechanics/generalized born surface area (MM/GBSA) binding free energy calculations were carried out to check the stability of bound complexes. The drug likeness and the pharmacokinetic properties of the selected molecules were also checked through the Lipinski filter and ADMETSAR analysis. All these bioactive compounds demonstrated strong binding affinity with AChE, BACE1 and synapsin I, II and III. The results showed UA and RA to be potential inhibitors of AChE and BACE1, exhibiting binding energies comparable to those of donepezil, used as a positive control. The drug likeness and pharmacokinetic properties of these compounds also demonstrated drug-like characteristics, indicating the need for further in vitro and in vivo investigations to ascertain their therapeutic potential for AD.