Last month, Kelly told ABC News' Diane Sawyer, "Ideally I would like to have that conversation with Gabby. I've flown in space three times. I don't have to do it again. My number-one goal is to make sure that my crew is safe and that they can execute this mission safely."
After the Tucson shooting, NASA, at Kelly's request, appointed a backup commander to train with the STS-134 crew. Rick Sturckow, a retired Marine Colonel, has flown four missions into space, and would have commanded the flight in Kelly's absence.
NASA gave Cdr. Kelly time to make his own decision.
Prior to the announcement, Chief Astronaut Peggy Whitson told ABC News, "Obviously, Mark has trained with this crew for over a year and so he is the ideal person for this crew from a mission risk perspective. It reduces our mission risk from that perspective, if we feel he is ready to go and would be undistracted by the circumstances then we will decide on that. But he, he is a tough guy, as you have seen. He's got his stuff together."
"Our job was to evaluate what was best for the mission," said Brent Jett, director of NASA flight crew operations. "We felt we covered all those areas to assess that."
Kelly and his crew have trained for a year and a half for the mission, so it won't take much for him to get back into the routine, and the Johnson Space Center is close enough to the hospital that he can see his wife often. His parents live in Houston, and Giffords' mother Gloria is also in Houston, so she is surrounded by family and friends.
Kelly's twin brother, Scott, is currently in orbit on the space station. The brothers had hoped to meet in space, but timing was not on their side -- Mark's mission was pushed back to April 19, and Scott returns to Earth in March.
In an interview from space, Scott Kelly told The Associated Press his brother is doing as well as anyone could expect. "His wife, the wounded congresswoman, is improving every day in rehab in Houston. He's concentrating on Gabby's care, but he's also been going back to work."
Mark Kelly's decision to go ahead with the April mission will force him to train rigorously, and then be gone from home for about a month. Astronauts go into quarantine about two weeks before flight, to protect against illnesses breaking out in orbit, where even a head cold can be debilitating.
Crews usually leave Houston for the Kennedy Space Center about five days before launch. The flight itself is currently planned to run 14 days, though shuttle landings are often delayed by weather. Some astronauts return to Houston the day they land, though many need a day or two to readapt to the Earth's gravity.
Dr. John Holcomb, the trauma surgeon heading Giffords' team at Memorial Hermann Hospital in Houston, said he was confident that Kelly would make the right decision for his family.
"I think that there's a certain amount of settling into a routine that happens once you're out of the ICU," Holcomb said, "and I think Capt. Kelly will get into a routine that he's comfortable with, that his wife's comfortable with, and that's obviously a very personal decision."