McCaul will head to Washington because he has no Democratic opponent for the 10th District seat in the Nov. 2 general election. McCaul had 64 percent of the vote and Streusand, 36 percent, according to the Texas Secretary of State.
McCaul and Streusand spent more than $5 million on their campaigns in the new district created during Republican redistricting last year.
The 10th District race was one of five Republican congressional runoffs Tuesday that determined nominees that were undecided after the March 9 primary.
Republicans also appeared to nominate state Rep. Arlene Wohlgemuth in the 17th District, former appeals court judge Louis Gohmert in the 1st District, Michael Thamm in the 15th District and James Hopson in the 28th District.
They will oppose Democratic incumbents Chet Edwards in the 17th District, Max Sandlin in the 1st District, Ruben Hinojosa in the 15th District and Henry Cuellar in the 28th District.