Yes. One person (U.S. or foreign) can form a corporation or LLC in Delaware. These are known as “single-member LLCs,” and can be used for everything from financing real estate transactions to solo consultant practices. However, it is still wise for single-member LLCs to have a written and executed Operating Agreement. Technically every Delaware LLC must have an operating agreement, while it is possible to make it verbal or oral, a written operating agreement will often be requested by those with whom you do business to show ownership and control.
Similarly regarding a corporation, one person can also hold all of the offices in the corporation, and be the only stockholder. Even a one person corporation should follow formalities and have bylaws and a stock certificate. One reason for this is because disregarding corporate formalities is one way to pierce the corporate veil and hold the stockholder personally liable for the corporation’s liabilities. Additionally, the corporation must hold an annual meeting of the sole stockholder and director and keep this record in a minute book.