The novel nature of SARS-CoV-2 calls for the development of efficient de novo drug design approaches. In this study, we propose an end-to-end framework, named CogMol (Controlled Generation of Molecules), for designing new drug-like small molecules targeting novel viral proteins with high affinity and off-target selectivity. CogMol combines adaptive pre-training of a molecular SMILES Variational Autoencoder (VAE) and an efficient multi-attribute controlled sampling scheme that uses guidance from attribute predictors trained on latent features. To generate novel and optimal drug-like molecules for unseen viral targets, CogMol leverages a protein-molecule binding affinity predictor that is trained using SMILES VAE embeddings and protein sequence embeddings learned unsupervised from a large corpus. We applied the CogMol framework to three SARS-CoV-2 target proteins: main protease, receptor-binding domain of the spike protein, and non-structural protein 9 replicase. The generated candidates are novel at both the molecular and chemical scaffold levels when compared to the training data. CogMol also includes insilico screening for assessing toxicity of parent molecules and their metabolites with a multi-task toxicity classifier, synthetic feasibility with a chemical retrosynthesis predictor, and target structure binding with docking simulations. Docking reveals favorable binding of generated molecules to the target protein structure, where 87--95\% of high affinity molecules showed docking free energy < -6 kcal/mol. When compared to approved drugs, the majority of designed compounds show low predicted parent molecule and metabolite toxicity and high predicted synthetic feasibility. In summary, CogMol can handle multi-constraint design of synthesizable, low-toxic, drug-like molecules with high target specificity and selectivity, even to novel protein target sequences, and does not need target-dependent fine-tuning of the framework or target structure information.