Ellis was born in Great Malvern in 1844. At school, he excelled in mathematics, and while he did study drawing, he disliked the emphasis placed on copying rather than original art.

In 1862, Ellis went to Kings College, London where during his second year earned the highest distinction in the Applied Sciences department in the college's history. He won all the scholarships offered by the college and was awarded the Associateship of Kings College after only two years' study, in recognition of his exceptional achievements.

After university, Ellis completed a pupilage under the railway engineer Sir John Fowler and became a partner in a firm of engineers. After several years there, Ellis decided that his calling lay in art. As he had sufficient means to support himself, he abandoned engineering and devoted his time to painting.

Several of Ellis's early oil paintings were shown at the Royal Academy. Despite this, he felt his technique needed improvement and moved to Paris to study under Leon Bonnat.

After his studies in Paris, Ellis began to travel. In 1878, he spent six months in Cyprus, then under British occupation. He returned with around fifty watercolors that were all sold to a dealer after their exhibition in Bond Street in 1879.

This success encouraged him to plan a more ambitious trip, and in 1879 he boarded a steamship for Alexandria with the aim of visiting Syria, Asia Minor and Mesopotamia. After his return to London, he showed about ninety watercolors from his travels, and sold them immediately. Ellis also wrote a two-volume illustrated account of his trip, 'On a Raft, and Through the Desert', which was published in 1881.

Ellis's next trip was to Egypt in the spring of 1882 where he spent three weeks at the Pyramids.

Several years later, Ellis made another trip to the eastern Mediterranean, where he spent time in Athens, and had three watercolors selected by George I of Greece.