WASHINGTON—President Trump is expected to nominate a former operations officer who played a critical role in the 2011 raid targeting Osama bin Laden to head of the U.S. Special Operations Command as part of a series of military promotions in coming months, according to U.S. officials.

The changes, which include commanders for the Middle East and Europe, will mark the administration’s largest imprint on military leadership thus far. The personnel moves stand to affect top officers overseeing conflicts in the Middle East, U.S....