This paper presents LLM2TEA, a Large Language Model (LLM) driven MultiTask Evolutionary Algorithm, representing the first agentic AI designer of its kind operating with generative evolutionary multitasking (GEM). LLM2TEA enables the crossbreeding of solutions from multiple domains, fostering novel solutions that transcend disciplinary boundaries. Of particular interest is the ability to discover designs that are both novel and conforming to real-world physical specifications. LLM2TEA comprises an LLM to generate genotype samples from text prompts describing target objects, a text-to-3D generative model to produce corresponding phenotypes, a classifier to interpret its semantic representations, and a computational simulator to assess its physical properties. Novel LLM-based multitask evolutionary operators are introduced to guide the search towards high-performing, practically viable designs. Experimental results in conceptual design optimization validate the effectiveness of LLM2TEA, showing 97% to 174% improvements in the diversity of novel designs over the current text-to-3D baseline. Moreover, over 73% of the generated designs outperform the top 1% of designs produced by the text-to-3D baseline in terms of physical performance. The designs produced by LLM2TEA are not only aesthetically creative but also functional in real-world contexts. Several of these designs have been successfully 3D printed, demonstrating the ability of our approach to transform AI-generated outputs into tangible, physical designs. These designs underscore the potential of LLM2TEA as a powerful tool for complex design optimization and discovery, capable of producing novel and physically viable designs.