Garza was 5-0 with a 1.24 ERA in his past six outings, and Navarro was behind the plate for each of those outings.
"Matty's my boy," Navarro said. "He's going to a contending team, and I know he's going to be just fine but it's sad to see a guy like Matty go. He's a guy who you can't stand him but you can't live without him. That's how I describe him, and I wish him nothing but the best. Hopefully, I'll see him down the road."
Navarro and Garza, who were teammates with the Rays, did joke about being part of a package deal.
"He was talking to me, saying, 'I'm going to ask for you,'" Navarro said.
What are the Rangers getting in Garza?
"I'm sure they've seen a lot themselves, with Garza pitching for the Rays," Cubs pitcher Jeff Samardzija said. "What Garza was 2 1/2 years ago, or a year and a half ago is different than he is today. He's a front-line guy, a leader in the clubhouse. He has no baggage, no sideshow. He just likes to talk.
"To tell you the truth, you need those guys," Samardzija said. "In a long season, you need guys who open their mouths and have fun and say some things that need to be said. That's just the truth and how it is. They're getting a great guy. He knows how to be a team player. He's going to fit in and do an amazing job, especially with the support he's going to get."
Navarro will miss the right-hander.
"I know he can get on a lot of people's nerves," Navarro said. "I understood him the best, and he knew I wasn't going to play around with him or bull crap with him. I was going to tell him the truth like it is and he was going to take it like a man."
Chris Rusin was promoted from Triple-A Iowa and inserted into the rotation on Monday against the D-backs in Garza's spot. How long he'll stay is up to the left-hander.
"It's going to test our depth," Samardzija said about losing Garza. "We'll see what we've got. ... People will just have to fill the holes and remember how last year was and try to prevent that."
Last year, the Cubs dealt two of their starters, Ryan Dempster and Paul Maholm, and lost Garza to an elbow injury for the final 2 1/2 months. The team finished 18-43 after the Trade Deadline, and lost 101 games that season.
"We just have to keep playing," outfielder Alfonso Soriano said. "We cannot control that situation, who goes, who stays. We have to keep playing hard in the field."
Navarro said he didn't expect to be switching teams.
"My wife thinks about it more than me because she's the one who has to pack the apartment," Navarro said. "We've got a great group of guys and hopefully we stay together for a little bit and turn this organization around."