We present ESP4ML, an open-source system-level design flow to build and program SoC architectures for embedded applications that require the hardware acceleration of machine learning and signal processing algorithms. We realized ESP4ML by combining two established open-source projects (ESP and HLS4ML) into a new, fully-automated design flow. For the SoC integration of accelerators generated by HLS4ML, we designed a set of new parameterized interface circuits synthesizable with high-level synthesis. For accelerator configuration and management, we developed an embedded software runtime system on top of Linux. With this HW/SW layer, we addressed the challenge of dynamically shaping the data traffic on a network-on-chip to activate and support the reconfigurable pipelines of accelerators that are needed by the application workloads currently running on the SoC. We demonstrate our vertically-integrated contributions with the FPGA-based implementations of complete SoC instances booting Linux and executing computer-vision applications that process images taken from the Google Street View database.