The launch of the NASA Earth Observing 1 (EO-1) platform in November 2000 marked the establishment of spaceborne hyperspectral technology for land imaging. The Hyperion sensor onboard EO-1 operates in the 0.4-2.5 micrometer spectral range, with 10 nanometer spectral resolution and 30-meter spatial resolution. Spectral unmixing has been one of the most successful approaches to analyze Hyperion data since its launch. It estimates the abundance of spectrally pure constituents (endmembers) in each observation collected by the sensor. Due to the high spectral dimensionality of Hyperion data, unmixing is a very time-consuming operation. In this paper, we develop a cloud implementation of a full hyperspectral unmixing chain made up of the following steps: 1) dimensionality reduction; 2) automatic endmember identification; and 3) fully constrained abundance estimation. The unmixing chain will be available online within the Web Coverage Processing Service (WCPS), an image processing framework that can run on the cloud, as part of the NASA SensorWeb suite of web services. The proposed implementation has been demonstrated using the EO-1 Hyperion imagery. Our experimental results with a hyperspectral scene collected over the Okavango Basin in Botswana suggest the (present and future) potential of spectral unmixing for improved exploitation of spaceborne hyperspectral data. The integration of the unmixing chain in the WCPS framework as part of the NASA SensorWeb suite of web services is just the start of an international collaboration in which many more processing algorithms will be made available to the community through this service. This paper is not so much focused on the theory and results of unmixing (widely demonstrated in other contributions) but about the process and added value of the proposed contribution for ground processing on the cloud and onboard migration of those algorithms to support the generation of low-latency products for new airborne/spaceborne missions.