Grammatical error correction can be viewed as a low-resource sequence-to-sequence task, because publicly available parallel corpora are limited. To tackle this challenge, we first generate erroneous versions of large unannotated corpora using a realistic noising function. The resulting parallel corpora are sub-sequently used to pre-train Transformer models. Then, by sequentially applying transfer learning, we adapt these models to the domain and style of the test set. Combined with a context-aware neural spellchecker, our system achieves competitive results in both restricted and low resource tracks in ACL 2019 BEAShared Task. We release all of our code and materials for reproducibility.