The fee for the USA international will be settled between €6.1m to €8.8m, reports The Athletic.
Bristol City had an attempt for Steffen fall through last summer.
"It gives a great feeling when you get such offers," Steffen said in September. "And I would also like to go to Europe. When that happens, I have little to say about it.
"But I do think that everything happens for a reason. It has not happened yet and so we move on to Columbus. I am well here and have great teammates and coaches. I'm happy."
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