Right-hander Rubby De La Rosa also joined the team at Dodger Stadium, but manager Chip Hale said De La Rosa won't be activated until he is ready to pitch.
De La Rosa has been on the DL since May 26 with inflammation in his right elbow. He threw 30 pitches, 22 for strikes, over two scoreless innings Monday for Class A Visalia.
Each of the players called up, except for Koch, had been with the D-backs previously this season.
Playing time will be difficult to come by for the position players, though the D-backs would like to see Haniger a bit more.
"There's going to be some pinch-hitting," Hale said. "We'll get them in there as best we can. If there's a matchup that looks good, we'll do it. If we need to give [Yasmany] Tomas or [A.J.} Pollock a rest, we've got guys to do it with now."
Steve Gilbert has covered the D-backs for MLB.com since 2001. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.