To understand the relationship between Orientalism and Imperialism, one has to understand the relationship between the "East" and the "West" as well as the imbalance of power between the two worlds. In his phenomenal work Orientalism (1978), Edward Said talks about “orientalism” as an ideology, discourse and body of knowledge created by westerners that misinterprets and then homogenises the eastern world and its culture, and justifies Western superiority and domination over the East. In Culture and Imperialism (1993), Said furthers his argument on orientalism by explaining how imperialism has created imaginary boundaries, power dynamics and perpetuated conflict and opposition between different parts of the world, between the Whites and the Blacks and between the colonised and the colonisers.
The relationship between orientalism and imperialism is simple. Said believes that orientalism supports colonisation and the imperial ideology. Oriental discourse makes generalisations about the cultural patterns in the non-Western world based on what was familiar to the Westerners and what wasn’t. The Eastern identity is represented as a set of decadent values, backwardness, barbarism, laziness, irrationalism, superstitions, lack of logic, etc., which, inevitably, the West thwarted and claimed was inferior to their own cultural identity. Since they felt it stood in staunch opposition to them, East became the “other” for the West. This knowledge of the Eastern reality was, however, incomplete and wrong. It not only created prejudices, but was also used to justify colonial subjugation of the East by the West.
Imperialism, which is the force behind colonisation, leads to power imbalance, and which along with hostility towards the unfamiliar Eastern reality, gives orientalists the privilege to place the orient below the occident. Put differently, it is imperialism that gives the authority and power to orientalists to estimate, homogenise, devalue and narrate the oriental reality to the western world. Orientalism, in this way, is nothing but a construct of imperialism.
I have moved this question to this group because I assume that you are asking about the concept of orientalism as pioneered by Said in this book.
If so, the relationship here is that orientalism has been used to justify and perpetuate imperialism. Said argues that orientalists have created a false dichotomy between the "East" and the "West" in order to show why imperialism is acceptable. Orientalists do this by positing that there is a fundamental difference between the East and the West. They say that all that is good is Western and all that is bad is Eastern. They see the East as having a culture that lacks the sort of energy and drive that has made the West great.
When the East is defined in this way, imperialism becomes acceptable. It is okay for the West to conquer and dominate because it has a superior culture.
So orientalism as a scholarly outlook is a means, Said says, of justifying imperialism.