Darwinism and Imperialism cannot be directly related, at least intellectually. The first is an scientific explanation for how evolution occurs, and the second describes the acquisition, or at least domination, of foreign peoples by more powerful nations. Historically, however, the two ideas were linked as a result of social Darwinism, the proponents of which (Darwin was not one) sought to apply the principles of evolution by natural selection to human society.
Some imperialists justified their position along social Darwinistic lines, which allowed them to frame human history as a struggle between peoples. Western nations, because of their alleged superior traits, had emerged as the more powerful, and it was only natural that they should exercise their power over weaker peoples, who had, according to social Darwinistic thought, somehow "lost." Additionally, many imperialists saw the struggle for colonies themselves among European nations in social Darwinistic terms.
It is important to note in closing that social Darwinism was and is not Darwinism, but rather a crude application of the terms of a biological theory to human life, an example of what some philosophers have called the "naturalistic fallacy." So the intellectual connection between actual Darwinism and imperialism is a very tenuous one, though the historical connection is undeniable. People appropriated some of the principles of a scientific theory describing a natural process to justify man-made decisions and practices.