Open a terminal window and type some of the text whose color you want to set the background the same as. Then open Terminal preferences.
Click the Window tab and then the Background Color. This brings up a color picker window. Click the magnifying glass in the upper left and move it over the text you want to match the color with. When you click on the text this will set the color you want. You could also set it directly in the RGB slider panel shown in the 2nd image which matches the text color from your image in the question.
Best Answer
From the Terminal Menu > Preferences > Profiles
Take your pick - fully customisable...