Professor Meese graduated first in his class with high honors in Ancient Greek from the College of William and Mary, where he also earned a secondary concentration in Economics. He then attended the University of Chicago Law School from which he graduated with honors, served as a Comment Editor on the Law Review, earned a John M. Olin Fellowship in Law & Economics, and was elected to Order of the Coif. After law school he clerked for Judge Frank H. Easterbrook of the U.S. Court of Appeals for the Seventh Circuit and Justice Antonin Scalia of the U.S. Supreme Court. He was admitted to the Virginia and District of Columbia Bars and practiced law at Skadden, Arps, Slate, Meagher and Flom in Washington, D.C.

Professor Meese joined the William & Mary faculty in 1995 and was a Visiting Professor of Law at the University of Virginia in the 2001-2002 academic year. He was the Cabell Research Professor of Law in 2001-2002, 2011-2012, 2013-2014, 2014-15, and 2018-19, and was the Tazewell Taylor Research Professor in 2016-17. He is a 2022-2023 Dean's Faculty Fellow.

Meese is the author or co-author of nearly 50 scholarly articles and essays appearing one or more times in The Green Bag, Antitrust Bulletin, Virginia Law & Business Review, Harvard Law Review Forum, Cornell Journal of Law and Public Policy, Hastings Law Journal, Antitrust Law Journal, Harvard Journal of Law and Public Policy, the Georgetown Law Journal, Law and Contemporary Problems, the William & Mary Bill of Rights Journal, and the University of Pennsylvania, Creighton, Fordham, Michigan, George Mason, Illinois, Boston University, Cornell, Southern California, Iowa, UCLA, North Carolina, Minnesota, Florida State, NYU, Wake Forest, University of Chicago, and William & Mary law reviews. He is a frequent lecturer on antitrust issues and has served as a referee for the Journal of Legal Studies, Journal of the History of Economic Thought, Journal of Competition Law and Economics, Harvard Law Review, Stanford Law Review, University of Chicago Law Review, Yale Law Journal and William & Mary Policy Review.

Professor Meese has been an active participant in Faculty Governance and Leadership at the University Level. Most recently, he served for two years as the Faculty representative on the College's Board of Visitors. He previously served as Vice President and then President of the Faculty Assembly, and he co-chaired the Committee on Religion in a Public University. He has twice chaired the College's Procedural Review Committee, co-chaired the Faculty and University Priorities Committee and served for three years on the University Planning Steering Committee.

Professor Meese received the Walter L. Williams Jr. Teaching Award in 2000 and received a Plumeri Fellowship for Faculty Excellence in 2010 and 2013.

Meese serves on the Boards of the Bork Foundation and the Antitrust Education Project. He is an Academic Affiliate of the International Center for Law & Economics and recently chaired the Executive Committee of the AALS Section on Antitrust and Economic Regulation. In the summer of 2013, Professor Meese participated in a National Endowment for the Humanities Summer Institute on the History of Political Economy at Duke University. He also served as a Senior Advisor to the Antitrust Modernization Commission from 2004-2007. In April, 2007, the Virginia Bar Association included Meese on a list of 11 candidates it recommended for nomination to the United States Court of Appeals for the Fourth Circuit. In 2017, Professor Meese received the William Small Award, conferred by the Society for the College, in recognition of his "professional commitment to the academic excellence of the College of William & Mary and to the furtherance of the education of his students."