Drug formulations for systemic drug delivery with improved stability and rapid onset of action are described herein. The formulations are administered sublingually or via subcutaneous injection. The formulations contain an active agent and one or more excipients, selected to increase the rate of dissolution. In the preferred embodiment, the drug is insulin, and the excipients include a zinc metal chelator such as EDTA and a solubilizing acid such as acetic acid, ascorbic acid, or citric acid.