Synthetic chemists have devoted tremendous effort towards the production of precision synthetic polymers with defined sequences and specific functions. However, the creation of a general technology that enables precise control over monomer sequence, with efficient isolation of the target polymers, is highly challenging. Here, we report a robust strategy for the production of sequence-defined synthetic polymers through a combination of liquid-phase synthesis and selective molecular sieving. The polymer is assembled in solution with real-time monitoring to ensure couplings proceed to completion, on a three-armed star-shaped macromolecule to maximize efficiency during the molecular sieving process. This approach is applied to the construction of sequence-defined polyethers, with side-arms at precisely defined locations that can undergo site-selective modification after polymerization. Using this versatile strategy, we have introduced structural and functional diversity into sequence-defined polyethers, unlocking their potential for real-life applications in nanotechnology, healthcare and information storage.