Quantitative MRI (qMRI) offers tissue-specific biomarkers that can be tracked over time or compared across populations; however, its adoption in clinical research is hindered by significant computational demands of parameter estimation. Images acquired at high spatial resolution or requiring fitting multiple parameters often require lengthy processing time, constraining their use in routine pipelines and slowing methodological innovation and clinical translation. We present GACELLE, an open source, GPU-accelerated framework for high-throughput qMRI analysis. GACELLE provides a stochastic gradient descent optimiser and a stochastic sampler in MATLAB, enabling fast parameter mapping, improved estimation robustness via spatial regularisation, and uncertainty quantification. GACELLE prioritises accessibility: users only need to provide a forward signal model, while GACELLE's backend manages computational parallelisation, automatic parameter updates, and memory-batching. The stochastic solver performs fully vectorised Markov chain Monte Carlo with identical likelihood on CPU and GPU, ensuring reproducibility across hardware. Benchmarking demonstrates up to 451-fold acceleration for the stochastic gradient descent solver and 14,380-fold acceleration for stochastic sampling compared to CPU-based estimation, without compromising accuracy. We demonstrated GACELLE's versatility on three representative qMRI models and on an image reconstruction task. Across these applications, GACELLE improves parameter precision, enhances test-retest reproducibility, and reduces noise in quantitative maps. By combining speed, usability and flexibility, GACELLE provides a generalisable optimisation framework for medical image analysis. It lowers the computational barrier for qMRI, paving the way for reproducible biomarker development, large-scale imaging studies, and clinical translation.