Transformer-based large language models (LLMs) encounter challenges in processing long sequences on edge devices due to the quadratic complexity of attention mechanisms and growing memory demands from Key-Value (KV) cache. Existing KV cache optimizations struggle with irreversible token eviction in long-output tasks, while alternative sequence modeling architectures prove costly to adopt within established Transformer infrastructure. We present EdgeInfinite, a memory-efficient solution for infinite contexts that integrates compressed memory into Transformer-based LLMs through a trainable memory-gating module. This approach maintains full compatibility with standard Transformer architectures, requiring fine-tuning only a small part of parameters, and enables selective activation of the memory-gating module for long and short context task routing. The experimental result shows that EdgeInfinite achieves comparable performance to baseline Transformer-based LLM on long context benchmarks while optimizing memory consumption and time to first token.