Van Dyken, 41, a six-time Olympic gold medallist, flew to her home state and went to her Scottsdale residence after making a television appearance in New York, her spokesman Mark Zimmerman said.
"Arizona is her home base and she's excited about coming home," he said.
She suffered a severed spinal cord in the June 6 vehicle crash in Arizona that left her paralysed from the waist down, and she has since chronicled her recovery process on social media.
After undergoing surgery to stabilise her spine, Van Dyken was taken from an Arizona medical facility to Colorado and spent two months in a specialised rehabilitation facility in suburban Denver.
She told NBC's "Today" show on Friday in New York that she was preparing for the trip to her home in Arizona since she arrived at the rehabilitation centre and that she hopes to one day walk again.
Van Dyken, who took her first steps two weeks ago with the help of a robotic device, said she is working with a trainer on muscle activation.
"He helped me get back to the Olympics after two shoulder surgeries, why can't he get me back up on my feet now?" she said on the programme. "We'll see what happens."
Known as a fierce competitor, Van Dyken was one of swimming's most decorated athletes during her glittering career. She won four gold medals in the 1996 Atlanta Olympics and another two at the 2000 Sydney games.
(Editing by Alex Dobuzinskis)
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