Hill has been on the shelf with a broken left hand since April 15. He was hit by a pitch on the hand April 9 against the Pirates.
"It's been a long time," Hill said. "These guys have been doing a great job; it's been tough to see how much fun these guys are having."
In six rehab games with Triple-A Reno, the second baseman went 9-for-24 with eight runs and six RBIs.
"I took some good swings; the timing was there," Hill said. "I got the amount of at-bats I wanted, so I'm good. It's all about how you feel. Hits are always nice -- you never complain about a hit -- but you know when your swing is there and feeling good."
To help protect the healing bone, Hill wear will padded batting gloves at the plate. In 36 at-bats to start the season before getting hurt, the 31-year-old collected 11 hits including three doubles and two homers.
"It'll be awesome to get him back," Paul Goldschmidt said. "Obviously he's a very good player. We all know what he can do. It's good to get him back."
Paterson made two appearances out of the bullpen for Arizona, allowing a run on two hits over 2 1/3 innings.
Tyler Emerick is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.