This work presents a dynamically reconfigurable architecture for Neural Network (NN) accelerators implemented in Field-Programmable Gate Array (FPGA) that can be applied in a variety of application scenarios. Although the concept of Dynamic Partial Reconfiguration (DPR) is increasingly used in NN accelerators, the throughput is usually lower than pure static designs. This work presents a dynamically reconfigurable energy-efficient accelerator architecture that does not sacrifice throughput performance. The proposed accelerator comprises reconfigurable processing engines and dynamically utilizes the device resources according to model parameters. Using the proposed architecture with DPR, different NN types and architectures can be realized on the same FPGA. Moreover, the proposed architecture maximizes throughput performance with design optimizations while considering the available resources on the hardware platform. We evaluate our design with different NN architectures for two different tasks. The first task is the image classification of two distinct datasets, and this requires switching between Convolutional Neural Network (CNN) architectures having different layer structures. The second task requires switching between NN architectures, namely a CNN architecture with high accuracy and throughput and a hybrid architecture that combines convolutional layers and an optimized Spiking Neural Network (SNN) architecture. We demonstrate throughput results from quickly reprogramming only a tiny part of the FPGA hardware using DPR. Experimental results show that the implemented designs achieve a 7× faster frame rate than current FPGA accelerators while being extremely flexible and using comparable resources.