The move boosts an injury situation at the position, bringing back a former fan favorite just more than a year after trading him.
The A's are sending Class A starter Dakota Bacus to the Nationals in the swap, while Washington is paying $995,000 to Oakland as its portion remaining on Suzuki's 2013 salary.
He left Chicago where the Nationals were playing and was set to join Oakland in Baltimore for a weekend series with the Orioles.
"It feels good," Suzuki said in the A's clubhouse. "I'm shocked to say the least. I mean I couldn't be happier to come back where it all started and help this team get into the playoffs."
He did, however, like playing in Washington. That made leaving a little bit more difficult.
"It's bittersweet," Suzuki said. "I wouldn't say glad for a change of scenery. I enjoyed my time there. Send to me to a place with a chance to win, and I'm all in."
The defending AL West champion A's began the day 2½ games back of Texas in the division race.
Suzuki, selected by the A's in the second round of the 2004 draft, spent parts of the past two seasons with Washington after six in Oakland. He's batting .222 with three homers and 25 RBIs in 79 games.
Suzuki, originally traded to the Nationals on Aug. 3, 2012, fills a need for the pennant race.
"He's terrific," A's manager Bob Melvin said of Suzuki. "The tough part about replacing a catcher as far along as the season we are, is the transition period with the pitchers.
"So, this one is an easy one. He's knows most of our guys -- a team leader, always has been. I don't know if the front office could get a better guy for us."
Suzuki is expected to start Saturday.
Norris was batting .232 with eight homers and 26 RBIs. Jaso could miss the remainder of the season with lingering concussion symptoms. He took a ball off his mask July 24 at Houston and complained of a headache.
Initially, Jaso was placed on the seven-day concussion list the following day, then transferred to the 15-day disabled list on Aug. 8.
Pittsburgh-based concussion expert Dr. Micky Collins doesn't expect the concussion to end his career. Jaso is batting .271 with three homers and 21 RBIs in 70 games.
The San Francisco Chronicle earlier reported the Suzuki trade.