Management of the plastic industry is a momentous challenge, one that pits enormous societal benefits against an accumulating reservoir of nearly indestructible waste. A promising strategy for recycling polyethylene (PE) and isotactic polypropylene (iPP), constituting roughly half the plastic produced annually worldwide, is melt blending for reformulation into useful products. Unfortunately, such blends are generally brittle and useless due to phase separation and mechanically weak domain interfaces. Recent studies have shown that addition of small amounts of semicrystalline PE-iPP block copolymers (ca. 1 wt%) to mixtures of these polyolefins results in ductility comparable to the pure materials. However, current methods for producing such additives rely on expensive reagents, prohibitively impacting the cost of recycling these inexpensive commodity plastics. Here, we describe an alternative strategy that exploits anionic polymerization of butadiene into block copolymers, with subsequent catalytic hydrogenation, yielding E and X blocks that are individually melt miscible with PE and iPP, where E and X are poly(ethylene-ran-ethylethylene) random copolymers with 6 wt% and 90 wt% ethylethylene repeat units, respectively. Cooling melt blended mixtures of PE and iPP containing 1 wt% of the triblock copolymer EXE of appropriate molecular weight, results in mechanical properties competitive with the component plastics. Blend toughness is obtained through interfacial topological entanglements of the amorphous X polymer and semicrystalline iPP, along with anchoring of the E blocks through cocrystallization with the PE homopolymer. Significantly, EXE can be inexpensively produced using currently practiced industrial scale polymerization methods, offering a practical approach to recycling the world's top two plastics.