It's an artifact of several unrelated events. These are generalizations because there are poor whites in cities and wealthy blacks in the 'burbs. But historically, educated people started moving to cities for higher paying jobs as the Industrial Revolution started roaring. Now by this time in America, Emancipation had already occurred but there were still huge populations of Blacks in the South. Around the turn of the century, a huge migration of African Americans started moving north. This was known as the Great Migration. This is different than the other huge movement of Blacks during the African Diaspora powered by slave trade.

The push North mainly is attributed to segregation, racism, rampant violence (which we would call terrorism now) and then ultimately the Great Depression... where poverty was so bad, most took a chance by moving North to cities to find work... any work. Some historians consider these two distinct events: fleeing from violence and fleeing from poverty. Social mobility was better by Southern standards for Blacks, but working conditions were still abysmal. Industrial decline started around the early 60's and once again threw many back into poverty, with nowhere left to turn. In both cases of poor whites and blacks, it is the result of shifting economies that left once prosperous industries in a tail spin as need for low-skill jobs dwindled.

There are a number of great source books on the subject:

1. J. Lawrence: The Great Migration
2. I. Wilkerson: The Warmth of other Suns
3. M. Chatelain: South Side Girls

Conversely, some African Americans stayed back and made fantastic middle-class lives in the segregated Deep South. A wonderful book in pictures was written by a good friend of mine, Shawn Wilson about it called Separate, But Equal and even made a documentary of the same name which is archived in the new museum in D.C.

The movement of millions of African Americans from the southern states to northern cities is a result of the Great Migration spanning the late 19th century into the 1960's. They were seeking job opportunities in urban factories and to escape racial terrorism and lynchings in the South (e.g. KKK). With the decline of American manufacturing from the 1970's onward, most of the urban working class jobs they sought disappeared resulting in urban poverty. White rural poverty is a bit different. Take for example the Appalachian region. Many of the poor white communities are descendants of 19th century miners and loggers. When those industries eventually failed, so too did the prosperity of those communities dependent on those jobs as sources of income. In both cases you have wealthy industrialists using poor people as cheap labor and discarding them afterwards.

Everyone makes some good points. One of many reasons that should be acknowledged that resulted in urban, primarily black poor areas was the rise of the suburbs and the effects of the GI bill after WWII. One effect of the GI bill was the allocation of low-cost mortgages. This spurred the efflux of people from the city to the suburbs. In practice this didn't apply to blacks. Te-Nahasi Coates explains redlining-

The FHA had adopted a system of maps that rated neighborhoods according to their perceived stability. On the maps, green areas, rated “A,” indicated “in demand” neighborhoods that, as one appraiser put it, lacked “a single foreigner or Negro.” These neighborhoods were considered excellent prospects for insurance. Neighborhoods where black people lived were rated “D” and were usually considered ineligible for FHA backing. They were colored in red. Neither the percentage of black people living there nor their social class mattered. Black people were viewed as a contagion. Redlining went beyond FHA-backed loans and spread to the entire mortgage industry, which was already rife with racism, excluding black people from most legitimate means of obtaining a mortgage.

So basically, white flight occurred and took with them a vast portion of the capital and opportunity and were barred from moving into more stable or emerging areas through institutionally sanctioned racial policy. You can imagine the implications from there.

I think it varies throughout different parts of the US. The US has seen many periods of migrations for economic, social, and political reasons: the idea of manifest destiny, fueled by gold and silver, brought many settlers west; Native American resettlement on reservations; and not to mention the forced migration of Africans to the southern US.

Pre-Civil War, African-American populations were primarily in the more rural and agricultural southern US. Until the Emancipation Proclamation, African-American slaves could be bought, sold, or traded to different parts of the country. Many white southern farmers owned just owned a few slaves to work their small farms. But there were also a handful of larger plantations witch could number in the hundreds. After the Civil War, many African-Americans stayed in their local region and industry - with many becoming sharecroppers or working for low wages for their former farms.

A century later, industrialization and two world wars fueled massive migrations to the more urban north or midwest. In the midwest, large factories with assembly lines employed millions of people, becoming dominant industries in cities like Detroit. African-American communities arose in many northern cities; communities like Harlem, New York became centers of African-American culture. However, still today African-American populations are still more concentrated in the southern US.

In my home state of Texas, there are still many rural African-American communities. Cotton was a major crop in central Texas after the civil war And although Texas did not have many large plantations, many African-American communities arose from small farms or ranches and sharecropping. In central Texas, competition for good, fertile land was high; the most fertile land often went to the Anglo-American, German, or Czech settlers. Sorry if this doesn't answer your question, but I hope it gives you some context on the variations of populations throughout the US

Nobody has really taken a stab about why poor whites tend to be more rural. The Homestead act opened up wide swaths of Western farm land to anyone who could live on the land long enough to stake their claim. This was an attractive thing for poor, European Immigrants as owning land was something that was a difficult and expensive proposition in Europe in the 19th Century.

If you take things back to before the Civil War, large swaths of rural areas in the country were completely off limits for Black people to own any land (it wasn't just a Southern thing either). By the time free blacks could own land, most of the country East of the Mississippi river was fairly settled and owned by Whites. During the Great Migration (which other folks have covered), there was some farmland open West of the Mississippi River and some Blacks did move to places like Kansas, where the [Exodusters] (https://www.kshs.org/kansapedia/exodusters/17162) settled.

There are still a good deal of poor, rural blacks in the South, but there was very little opportunity for black folks to move into rural areas in most of the country.

There is most likely a whole new post/thread that could be made to discuss how large sections of rural areas have become poorer over the last 100 years. My quick summation of it is a combination of Brain Drain, better opportunity for Middle Class folks to move to urban areas, and a great technological leap in farm technology. Essentially few with the means willingly remain in a majority of these rural areas.

For most of the United States' history, blacks were only allowed to live in specific areas. Many counties and nearly all cities had sundown laws on the books, prohibiting blacks from remaining after dark. Most of these laws were overridden by Title VIII of the Civil Rights Act of 1968, but some related practices such as redlining continued up until at least the 1990s.

So, yeah, it was deliberate.

James Loewen's Sundown Towns: A Hidden Dimension of American Racism is a good book on the subject.