Who established judical review as a power of the supreme court?

Fourth Chief Justice John Marshall presided over the US Supreme Court when he formally claimed the courts' right to exercise judicial review in his opinion for the case Marbury v. Madison, (1803).

Contrary to popular belief, Marbury was the not first case in which the Supreme Court practiced judicial review, just the first time they declared an Act of Congress unconstitutional (Judiciary Act of 1789, § 13). A Circuit Court overturned a piece federal legislation in the late 18th century, and Congress accepted the decision without argument.

Judicial Review is a carryover from English common law practices that was adopted by the American courts.