Both have been drawn together because they are unseeded following bad form and injury problems.
Agassi returns to competition more than two months after his last encounter against Germany's Tommy Haas in the third round of the Indian Wells Masters.
The American chose to miss the entire clay-court season in order to rest his troublesome back and get the best out of the summer season.
ATP Queen's Club
Hewitt king of Queen's
18/06/2006 AT 14:29
Elsewhere, Greg Rusedski will meet French qualifier Antony Dupuis.
Meanwhile, Twice Roland Garros champion Rafael Nadal, Andy Roddick, James Blake, Ivan Ljubicic and Lleyton Hewitt have all been given first-round byes.
ATP Queen's Club
Hewitt aiming to end drought against Blake
18/06/2006 AT 10:34
ATP Queen's Club
Hewitt into 4th Queen's final
17/06/2006 AT 19:34