The House approved the measure, introduced by Arizona Sens. John McCain and Jon Kyl, on a 429-0 vote. The Senate passed it last week.
Construction is to begin in July on the courthouse that Roll, 63 when he died, had advocated and recently approved the design for.
Roll, who was appointed to the federal bench by President George H.W. Bush in 1991, was attending a meet-and-greet held by Giffords at a Tucson supermarket when the alleged gunman, Jared Loughner, opened fire. Giffords was shot in the head and 12 others were wounded.