Shays had been the only Republican from New England in the House since the 2006 election. He has represented the 4th District in eastern Connecticut's New York City suburbs since 1987.
Himes, a former Goldman Sachs executive and director of a non-profit housing corporation, was successful in his first run for political office, The Bridgeport Times reported.
"I have always known you can have elections you can win and you can have elections you can lose," Shays said as he conceded the race before supporters in Norwalk.
Jessica Simpson shares three-way kiss with friends in photo
Scarlett Johansson steps out with fiance after pregnancy reveal