Electroencephalography (EEG) signals are easily corrupted by various artifacts, making artifact removal crucial for improving signal quality in scenarios such as disease diagnosis and brain-computer interface (BCI). In this paper, we present a fully convolutional neural architecture, called DTP-Net, which consists of a Densely Connected Temporal Pyramid (DTP) sandwiched between a pair of learnable time-frequency transformations for end-to-end electroencephalogram (EEG) denoising. The proposed method first transforms a single-channel EEG signal of arbitrary length into the time-frequency domain via an Encoder layer. Then, noises, such as ocular and muscle artifacts, are extracted by DTP in a multi-scale fashion and reduced. Finally, a Decoder layer is employed to reconstruct the artifact-reduced EEG signal. Additionally, we conduct an in-depth analysis of the representation learning behavior of each module in DTP-Net to substantiate its robustness and reliability. Extensive experiments conducted on two public semi-simulated datasets demonstrate the effective artifact removal performance of DTP-Net, which outperforms state-of-art approaches. Experimental results demonstrate cleaner waveforms and significant improvement in Signal-to-Noise Ratio (SNR) and Relative Root Mean Square Error (RRMSE) after denoised by the proposed model. Moreover, the proposed DTP-Net is applied in a specific BCI downstream task, improving the classification accuracy by up to 5.55% compared to that of the raw signals, validating its potential applications in the fields of EEG-based neuroscience and neuro-engineering.