The Pirates will receive young pitchers Wil Crowe and Eddy Yean in return for Bell. Crowe made his debut with the Nationals last season.
"We are thrilled to be adding a player of Josh Bell's caliber to our team," Nationals general manager Mike Rizzo said in a statement. "He adds a switch-hitting power bat to our lineup. And we know Josh will be an outstanding addition to our clubhouse and our community."
The 28-year-old Bell was an All-Star selection in 2019 after a strong first half in which he recorded a .302 batting average with 27 home runs and 84 RBIs.
Bell, however, has struggled to keep that form over the last year-plus, as he hit .233 with 10 home runs during an injury-riddled second half of the 2019 campaign. He had only eight homers while batting a career-worst .226 in 57 games for the Pirates last season.
"In order to build that winning team and get to that winning team, it's going to require some difficult decisions at times," Pirates general manager Ben Cherington said. "This is one of those.
"I believe what Pirates fans want is a winning team more than they want to root for a single player, even one who is a really good guy and a good player. If we think about that, that's how we see it."
Bell is under contractual control through at least the 2022 season.
Crowe, 26, was one of the Nationals' top pitching prospects. He had a 0-2 record and 11.88 ERA in three starts for Washington in 2020.
The 19-year-old Yean signed with the Nationals as an undrafted free agent in 2020. He has posted a 3-5 record with 75 strikeouts while playing in the low minors.