The Nationals announced the deal Thursday before their game at the Milwaukee Brewers.
Washington also transferred outfielder Nate McClouth from the 15-day disabled list to the 60-day DL and the team said it would make another move later Thursday to make room on the 25-man roster for Carpenter.
Carpenter was designated for assignment by the Yankees on June 3, after going 0-1 with a 4.82 ERA in 22 games this season.
He is 11-11 with a 2.73 ERA in 210 career appearances for four major league clubs.
Renda was a second-round draft pick in 2012.