Rodriguez, 31, appeared in 25 games for the Brewers this season with a 1.09 ERA and 10 saves. Signed in April to a minor-league contract, Rodriguez was promoted to the Brewers on May 15.
"He's been nothing but a real professional with us," Brewers general manager Doug Melvin said. "He's a great competitor, and we like him a lot. It's unfortunate our season is where we are at and moves like this have to be made. We feel very good getting a young player like Nick. He's a third-baseman, a left-handed bat, and he'll fit in with some of our younger players."
Melvin set Tuesday as the deadline for the six interested teams to give the Brewers their final offer for Rodriguez. Milwaukee has long coveted Delmonico, but were told as recent as three weeks ago that he was not available.
The Brewers narrowed down the interested parties to three finalists, all American League clubs.
"There was enough traffic on K-Rod that we were able to extract what we consider a good player that still has to develop," Melvin said. "(He's) a good player that has a chance to be a major-league player."
For Rodriguez, the move to Baltimore is bittersweet. He's pleased to be going to a team in the middle of a pennant race, but didn't want to leave the place that gave him a chance to return to the big leagues this year.
"I'm sad, I'm not going to lie to you," Rodriguez said. "I'm extremely sad. I definitely did not want to leave the organization, but at the same time I understand this is a business. I do understand this is part of the game. I knew coming in that I could end up somewhere else.
"At the same time, it's a new opportunity for me. I'm looking forward to the challenge. Hopefully I can do my best and get my job done."
It has been a whirlwind season for Rodriguez. After finishing last season with a 4.38 ERA for the Brewers, Rodriguez went unsigned through spring training and into the regular season.
Needing relief help at the time, Milwaukee signed Rodriguez to a minor-league contract on April 17 and had 30 days to call him up to the big leagues with a salary of $2 million or release him. The move has paid dividends; Rodriguez hasn't allowed a run in 22 of his 25 appearances this season.
"I would have rather been in a pennant race and keeping him, but that's the way things go," Melvin said. "I informed him and he was a real pro. I told him he gets a chance to go with a team that's on a pretty good roll right now. I've spent years in Baltimore, and it's a great experience when you are in a pennant race there.
"He's pitching really well right now. I think he's the type of guy that can be a difference maker. When you get into postseason or into pennant races in August and September, you always need more than one guy that can pitch in the ninth inning. He's capable of doing that."
Collecting his 300th save on June 22, Rodriguez is tied with Jeff Montgomery for 21st on the all-time saves list with 304.
"Before I was in the minor leagues, I was at home," Rodriguez said. "That tells you anything can happen. I wish I could have control over it, but unfortunately I don't. I just have to go with it and it's another chapter of my life.
"I'm leaving sad. It's not like I'm leaving happy because I'm going somewhere else, it's not like that. I have to take it for what it is. I'm going to have good memories, leave a lot of good friends behind, but you never know what's going to happen next year."
First acquired on July 12, 2011 from the New York Mets, Rodriguez was outstanding in the team's run to the division title and the National League Championship Series that season. He had a 1.86 ERA in 31 regular-season games with the Brewers and yielded just one run in five playoff innings.
Though pitching in the playoffs is a memory Rodriguez won't forget, he's most thankful for the Brewers giving him a chance to continue his career when the rest of the league considered him done.
"In a big way," Rodriguez said when asked if he's thankful for the organization taking a chance on him. "The first thing I told the GM and the manager was thank you for this opportunity to wear a uni. That's something that I take a lot of pride in and will always be in the back of my mind."
The son of former University of Tennessee baseball coach Rod Delmonico, the 21-year-old Nick Delmonico fell to the sixth round of the 2011 Major League Baseball first-year draft due to sign-ability issues.
Baltimore eventually gave Delmonico $1.5 million to sign with the organization. Last season, Delmonico hit .249 with 11 home runs and 54 RBI for Single-A Delmarva. Moving up the ladder to Class-A Advanced Frederick, Delmonico is hitting .244 with 13 home runs and 30 RBI in 60 games this season.
"I didn't know I was traded straight up for him," Delmonico told MASNSports.com. "When you see that on paper, it's pretty cool."
Ranked as the 4th overall prospect in Baltimore's organization by Baseball America, Delmonico will report to Class-A Advanced Brevard County.
"Nick Delmonico shows a lot of promise as a hitter," Orioles general manager Dan Duquette told MLB.com. "But the Major League club needed a little more depth for our pitching staff to accomplish what we want to accomplish this year."
Despite all the challenges 2013 has presented, Rodriguez thinks the organization is going to come through just fine.
"They are going to be OK," Rodriguez said. "Any ball club goes through adversity. They are going through some right now, but they are going to be fine. This is going to be behind them in a week. A lot of stuff will go away. They are going to continue to play. It's not like they've lost confidence at all."