Spiking Large Language Models (LLMs) have emerged as an energy-efficient alternative to conventional LLMs through their event-driven computation. To effectively obtain spiking LLMs, researchers develop different ANN-to-SNN conversion methods by leveraging pre-trained ANN parameters while inheriting the energy efficiency of SNN. However, existing conversion methods struggle with extreme activation outliers and incompatible nonlinear operations of ANN-based LLMs. To address this, we propose a loss-less ANN-SNN conversion for fully spike-driven LLMs, termed LAS. Specifically, LAS introduces two novel neurons to convert the activation outlier and nonlinear operation of ANN-based LLMs. Moreover, LAS tailors the spike-equivalent Transformer components for spiking LLMs, which can ensure full spiking conversion without any loss of performance. Experimental results on six language models and two vision-language models demonstrate that LAS achieves loss-less conversion. Notably, on OPT-66B, LAS even improves the accuracy of 2% on the WSC task. In addition, the parameter and ablation studies further verify the effectiveness of LAS. Code is available at https://github.com/lc783/LAS.