When Marko Cheseto, who competed on the track for the University of Alaska Anchorage, disappeared he was not wearing protective winter clothing.
After he was found on 9 November he was suffering from hypothermia and severe frostbite on his feet and hands.
University officials say his hands are expected to fully recover.
His disappearance, a day after the university's cross-country team's return from a triumphant championship in Washington State, sparked an intensive search for the 28-year-old athlete.
The University Alaska Anchorage (UAA) said Mr Cheseto, who is studying nursing and nutrition, will remain in hospital for some time to come.
In a statement on the university's website, Mr Cheseto thanked the university and volunteers who searched for him.
"While I am still recovering - both physically and emotionally - I will do my very best to give back to the community that has helped me so much and to my home country, Kenya. I sincerely apologise for any problems that I may have caused."
Mr Cheseto has reportedly been suffering from depression since fellow UAA student runner William Ritekwiang, from his hometown of Kapenguria, took his own life in February.
After his 48 hours out in freezing temperatures, Mr Cheseto stumbled into a hotel near the UAA campus in the early hours of Wednesday 9 November.
The hotel's night manager told the Anchorage Daily News that the paramedic team could not remove his sports shoes as they were frozen to his feet.
"He seems very upbeat and anxious to get on with a rehabilitation programme," Steve Cobb, UAA's director of athletics, is quoted by Reuters news agency as saying.
During his time at the university, Mr Cheseto set the record for the Anchorage Mayor's Half Marathon in 2010 and has won several All-American student athletic titles.