During the second term of Ronald Reagan from 1986 to 1988, he served in the White House as Senior Associate Counsel to the President.

From 1977 to 1986, Cox was first an associate and then partner with the international law firm of Latham & Watkins. At the time of his retirement in 1986 he was the Partner in Charge of the Corporate Department in the Orange County office, and served as a member of the firm's national management.

In 1984, Cox co-founded Context Corporation, which produced daily English reproductions of the leading state-controlled newspaper in the Soviet Union, Pravda. The publication was used chiefly by U.S. universities and U.S. government agencies, and was eventually distributed to customers in 36 countries around the world. The company had no connection to the Soviet government.

In 1982-83, Cox took a leave of absence from Latham & Watkins to teach federal income tax at Harvard Business School.

After graduating from St. Thomas Academy in St. Paul, Minnesota in 1970, Cox earned his B.A. at the University of Southern California in 1973, following an accelerated three-year course. In 1977 he earned both an M.B.A. from Harvard Business School and a J.D. from Harvard Law School, where he was an Editor of the Harvard Law Review.

For 10 of his 17 years in the Congress, from 1995 to 2005, Cox served in the House Majority Leadership as Chairman of the House Republican Policy Committee, the 5th ranking elected leadership position (behind the Speaker, the Majority Leader, the Majority Whip, and the Chair of the House Republican Conference). He was Chairman of the House Committee on Homeland Security, and also Chairman of the Select Committee on U.S. National Security that produced the Cox report, an indictment of Chinese espionage and of security failures at several U.S. national laboratories.

When Congress established the Bipartisan Study Group on Enhancing Multilateral Export Controls through federal legislation in 1999, Cox was tapped as Co-Chairman. The group published a unanimous report in 2001 recommending wholesale modernization of U.S. export controls. In 1994 he was appointed by President Clinton to the Bipartisan Commission on Entitlement and Tax Reform, which in 1995 published a unanimous report warning that the nation cannot continue to allow entitlement programs to consume a rapidly increasing share of the federal budget. Cox also served as Chairman of the Select Committee on Homeland Security (the predecessor to the permanent House Committee); Chairman of the Task Force on Capital Markets; and Chairman of the Task Force on Budget Process Reform.

Among Cox's notable legislative successes is the Internet Tax Freedom Act, a 1998 law prohibiting federal, state, and local government taxation of Internet access and banning Internet-only levies such as email taxes, bit taxes, and bandwidth taxes. With U.S. Rep. Barney Frank (D-MA) as his chief co-sponsor, Cox authored legislation in 1997 to privatize the National Helium Reserve, which was then $1.4 billion in debt to taxpayers. As of 2004, this was the third-largest privatization in U.S. history, surpassing the value of the 1988 Conrail privatization. Cox also wrote the only law that was enacted over President Bill Clinton's veto, the Private Securities Litigation Reform Act of 1995, aimed at protecting investors from fraudulent and extortionate lawsuits.

In 1989 Polish President Lech Wałęsa joined Cox in a Washington ceremony marking the enactment of Cox's legislation establishing the Polish-American Enterprise Fund. Together with the Baltic-American Enterprise Fund, the Hungarian-American Enterprise Fund, and seven other enterprise funds in Central and Eastern Europe and the former Soviet Union, the Cox legislation, incorporated in the Support Eastern European Democracy (SEED) Act, matched U.S. foreign aid with venture capital in the newly free countries of the former Warsaw Pact. This was the first foreign assistance program in history to return a significant amount of money to the U.S. Treasury.

Cox is married to the former Rebecca Gernhardt, a Continental Airlines executive and former Assistant US Secretary of Transportation. The two met in the Reagan White House, where she served as Director of the Office of Public Liaison. They have three children.