Fox will make his debut appearance at a PGA Tour event in the United States courtesy of his exceptional form on the European Tour.
The big-hitting Fox's missed cut at last month's British Open was preceded by three top-six finishes in France, Ireland and Scotland.
The 30-year-old's world ranking dipped inside the top-100 for the first time but has slipped back to 101st, 14 slots behind Lee.
Both Kiwis have been handed late tee-off times for the first day.
Lee's playing partners are Australian Marc Leishman and Indian Anirban Lahiri while Fox is grouped with American JJ Wood and China's Hao Tong Li.
Much interest will centre on 24-year-old British Open champion Jordan Spieth.
If successful, Spieth will surpass fellow-American Tiger Woods and became the youngest career grand slam winner in golf history.
- AAP