The student, Kevin MacDonald, was taken to Seattle's Harborview Medical Center with serious injuries after emergency crews were called at 4:30 a.m. Saturday, but he died later that day.
A press release issued by the fraternity said MacDonald was getting in or out of bed and fell out the window. Other fraternity members were awakened by the fall and called 911.
Seattle police spokesman Mark Jamieson agreed that the fall appeared to be the result of a tragic accident.
"We did not find evidence of foul play or criminal intent here," he said.
Investigators have not located any witnesses to the fall. MacDonald was alone in the room when he fell, the fraternity said.
MacDonald was a junior at the UW, majoring in psychology. Born in Renton, he moved with his family to Kent while young and attended Kent Meridian High School. He then attended Bellevue Community College, transferring to the UW in 2007.
MacDonald was keenly interested in all kinds of sports and was an athlete at Kent Meridian, according to postings he made on the Internet.
"You can sum up my life with three categories: sports, music, friends/family," he wrote of himself on his fraternity's web site. "I love sports of all kinds; playing and watching. I also love to snowboard."
He died at Harborview Medical Center at about 6:30 p.m. Saturday with his family and fraternity brothers at his side.
"Our hearts and prayers are with Kevin’s family. Our entire chapter has received hundreds of calls from around the Greek and university community to say that we and his family were in their thoughts," said Eliab Sisay, Alpha Sigma Phi chapter president.
"Today our men demonstrated true brotherhood for one another and for Kevin’s family. The impact of this incident is overwhelming. I just can’t find the words to express the sadness I and the entire chapter feel."
The news of MacDonald's death came as thousands of seniors graduated from the University of Washington on Saturday, casting a pall on an otherwise joyful occasion.
"Right now, I really feel sad. (It's) shocking really ... I feel bad for this poor student," said Hsiao-Ning Lin, a graduating senior.