The 10th Congressional District seat was vacated last week with Mr. Norwood's death.
Secretary of State Karen Handel has agreed to set the qualifying date after the General Assembly session concludes.
That would allow state legislators who might run to fulfill their duties in the Assembly and give candidates time to campaign.
If a runoff is required, it would occur four weeks later, July 17.
State Sens. Jim Whitehead, of Evans, and Ralph Hudgens, of Comer, have said they plan to run for the position.
Because they must resign the legislative seats to run for Congress, the special election also would fill those vacancies.
Also on Thursday, Augusta businesswoman and Republican Jackie Poteet, 66, announced her candidacy.
Mrs. Poteet started Apartment Finders in Augusta in 1973 and Marjac Publications in 1979 before branching out to publish apartment guides in the Macon-Warner Robins area and Savannah. She sold her companies to a national concern in 2001.
Mrs. Poteet has never run for public office before, which she says might be a plus.
"We need fresh ideas, new ways of looking at things," she said. "I can do this, I know I can. I enjoy a challenge."
Dr. Paul Broun, a Republican from Athens, and Thomson jeweler Terry Holley, a Democrat, have announced their candidacies.
The June 19 date - more than four months after Mr. Norwood succumbed to cancer - is later than most past special elections.
Mr. Norwood's staff will continue to operate at the Capitol until a successor is chosen.
June 19 is one of four days in the year when cities and counties are allowed to hold municipal elections, so other counties may save additional money by including local votes.
Morris News Service reports were used in this story.
Reach Sylvia Cooper at (706) 823-3228 or email@example.com.