The Cubs sent Class A infielder Andruw Monasterio and a player to be named later or cash considerations to Washington for Murphy. The Cardinals sent cash considerations to the Nationals for Adams.
It is unclear where Murphy will play in Chicago. Javier Baez, who is having an MVP-caliber season (.289 batting average, 25 home runs, 89 RBIs, 20 steals), is the Cubs' primary second baseman. Murphy also has experience playing third, and Cubs starting third baseman Kris Bryant is currently on the disabled list with a shoulder injury.
"We were certainly looking to jump-start the offense," Cubs president Theo Epstein said before the team's 2-1 loss to the Tigers on Tuesday night. "We've been scuffling lately. We thought the addition of consistent, high-level, professional at-bats would help us. Daniel Murphy has as good at-bats as anyone in the game."
The Cubs rank 14th in the National League in scoring this month (3.2 runs per game) after entering the month first (5.0). And with Tuesday's defeat, they have now scored just one run in five straight games, the second time that's happened in franchise history.
"I was surprised. I think everyone was, to get that great of an offensive player at this point in the season," the Cubs' Ben Zobrist said. "We'll find a way to make him fit in the lineup. It will be fun playing alongside of him.
"If we were killing it offensively, maybe we wouldn't be doing it, but we haven't been. We could use a little boost. Hopefully he can provide it for us."
Nationals general manager Mike Rizzo said the trades give his team financial flexibility for the 2019 season. He said he believes in the players remaining on his roster.
"I still think today we have the talent base on this team to play competitive games at the end of the season. ... I know what the standings say and what the calendar says, but the talent level in that locker room is still great," he said.
In an open letter to the team's fans, Nationals owner Mark D. Lerner explained the reasoning behind the trades, writing that Washington "gambled" at the July 31 trade deadline by not trading some players then.
"When something isn't working, you evaluate the situation and take the necessary steps to improve it. You don't just stand by, cross your fingers, and hope for the best. Unfortunately, in this case, that means making very tough decisions about our roster," Lerner wrote.
"I believed in this team, and would have loved to see them all play healthy together this season. However, the time has come for us to make decisions that will bolster our roster for next season and beyond. This is about giving us some roster flexibility, giving us the opportunity to see some of our young talent, and seeing if we can still find a combination or two that could spark a difference."
Murphy, a career .299 hitter, is batting .300 this season with 6 home runs and 29 RBIs in 56 games. He will be a free agent after this season.
Murphy said he was "surprised" to learn he was traded and called the move "bittersweet."
"I think I was a bit surprised. I'm going to be honest with you: I didn't think I was going to get claimed. I thought I would slide right through. But yeah, it was a surprise to me. And my thoughts are, it was really bittersweet," he said.
"Sat at this podium probably 2½ years ago. The Washington Nationals were the only offer I had, and so they took a chance on me three years ago, and I feel very disappointed in myself that it kind of came to this point. No ill will whatsoever. It was just unfortunate that this was an option. So yeah, I was surprised. Sad. But that's baseball. It wasn't anything malicious in nature."
Murphy is hitting .340 since the All-Star break, ranking 10th in the majors. Over the past three seasons, Murphy is hitting .366 with runners in scoring position, the best mark by anyone with at least 500 plate appearances.
The three-time All-Star was the National League Championship Series MVP in 2015 when, with the New York Mets, he hit four home runs in a four-game sweep of the Cubs. He set a major league record by hitting home runs in six straight playoff games that year.
"It's really fun to watch him hit," Cubs manager Joe Maddon said. "He always throws out a good at-bat. I don't care if the pitcher is left- or right-handed. I don't care if he's throwing hard or soft. The guy knows what he's doing at the plate."
Monasterio, 21, is hitting .263 with 3 home runs, 31 RBIs and 10 stolen bases for the Cubs' affiliate in Myrtle Beach this season.
Adams, who began his career with the Cardinals, is hitting .257 with 18 home runs and 48 RBIs in 94 games. He is 0-for-21 dating back to Aug. 5 and has started only four games over that span, losing playing time at first base to Ryan Zimmerman.
Cardinals interim manager Mike Shildt said Adams will join the team at Dodger Stadium on Wednesday and be activated for the series finale against Los Angeles.
"We're talking about a guy who's a proven big league, accomplished hitter,'' Shildt said. "Done it for us for years. Done it since he's left us. He's definitely a perfect fit for what we're trying to accomplish here.''
The Nationals have been a disappointment this season and are currently a game under .500 at 62-63. They are 7½ games out in the National League East. The Cubs lead the NL Central with a 71-52 record. The Cardinals, in second place in the NL Central at 70-57, are locked in a tight race with Milwaukee for the first NL wild-card spot.
The Nationals, who had finished first in the NL East in 2016 and '17, fired manager Dusty Baker after losing to the Cubs in five games in the NL Division Series last year. They replaced him with rookie manager Dave Martinez, who had been the Cubs' bench coach.
Nationals outfielder Bryce Harper, the 2015 NL MVP, said Tuesday the Nationals aren't giving up on the season and that he didn't believe he'd be traded, like Murphy and Adams were.
"I didn't think I was going leave at all or move at all. I think for me it's coming into the clubhouse every single day and trying to win ballgames and do the things I can to help this team win on a daily basis," he said. "I think I'm part of this organization; I've been part of this organization for seven years. I look forward to coming and doing my job every single day. I had no fear of being traded or let go on waivers or anything like that."
To fill the spots created by the departures of Murphy and Adams, the Nationals recalled infielder Adrian Sanchez and outfielder Andrew Stevenson from Triple-A Syracuse.
Martinez came on in relief Tuesday night against the Dodgers, pitching 1.1 innings before getting hit in the upper body by a comebacker from Joc Pederson in the eighth. Martinez was knocked down and writhed on the ground as his teammates and a trainer ran to him. He soon got up and walked off under his own power as the inning ended. X-rays were negative, and the Cardinals came away with the 5-2 win.
ESPN's Eddie Matz, Jesse Rogers, Stats & Information and The Associated Press contributed to this report.