A Giffords spokesman said the astronaut and his wife held hands for two hours Thursday evening.
A cheering crowd of several hundred workers and family members greeted the six astronauts as they returned home to Houston.
Giffords, who was critically wounded in a January shooting, didn't attend the public celebration.
The couple had last been together the day before /*Endeavour*/'s May 16 launch. Then Endeavour blasted off and spent 18 days in space. It was Endeavour's final flight after 19 years.
Kelly said this is not the end of Endeavour's career. He spoke of its new mission at the California Science Center in Los Angeles.
"Its future is going to be to continue to inspire young people to pursue careers in science, engineering and math, and it's going to do that for a very long time," said Kelly.
Endeavour has been moved into its processing bay. It will take many months to prepare it for museum display. It is expected to arrive in /*Los Angeles*/ in fall 2012.
The Associated Press contributed to this story