Alzheimer’s disease (AD) is the most common form of dementia with no cure so far, probably due to the complexity of this multifactorial disease with diverse processes associated with its origin and progress. Several neuropathological hallmarks have been identified that encourage the search for new multitarget drugs. Therefore, following a multitarget approach, nine rivastigmine–indole (RIV-IND) hybrids (5a1-3, 5b1-3, 5c1-3) were designed, synthesized and evaluated for their multiple biological properties and free radical scavenging activity, as potential multitarget anti-AD drugs. The molecular docking studies of these hybrids on the active center of acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) suggest their capacity to act as dual enzyme inhibitors with probable greater disease-modifying impact relative to AChE-selective FDA-approved drugs. Compounds 5a3 (IC50 = 10.9 µM) and 5c3 (IC50 = 26.8 µM) revealed higher AChE inhibition than the parent RIV drug. Radical scavenging assays demonstrated that all the hybrids containing a hydroxyl substituent in the IND moiety (5a2-3, 5b2-3, 5c2-3) have good antioxidant activity (EC50 7.8–20.7 µM). The most effective inhibitors of Aβ42 self-aggregation are 5a3, 5b3 and 5c3 (47.8–55.5%), and compounds 5b2 and 5c2 can prevent the toxicity induced by Aβ1-42 to cells. The in silico evaluation of the drug-likeness of the hybrids also showed that all the compounds seem to have potential oral availability. Overall, within this class of RIV-IND hybrids, 5a3 and 5c3 appear as lead compounds for anti-AD drug candidates, deserving further investigation.