The network said that Kelly spoke to Sawyer on Saturday at the hospital where Giffords continues to recover from being shot in the head on Jan. 8.
ABC said Sunday the interview will air in a prime-time special on Tuesday night and in various ABC News broadcasts, starting Tuesday with "Good Morning America."
Kelly was interviewed briefly off-camera last week by CNN's Sanjay Gupta.
In the prime-time special, titled "The Congresswoman and the Astronaut: An American Story of Love and Strength," Kelly talks about the moment he heard his wife was shot, the bedside vigil he has kept and how the support of the nation has affected them, the network said.
It's a big get for Sawyer, the "World News" anchor who has long been competitive in the race for major newsmaker interviews.
ABC was the only national TV news division not to falsely report Giffords had died in the hours after the shooting, although its website briefly did. Kelly called an ABC affiliate in Houston when those reports were being broadcast to say that his wife was still alive.