San Diego got the 30-year-old Manaea and minor league right-hander Aaron Holiday from Oakland for pitching prospect Adrian Martinez and minor league infielder Euribiel Angeles.
Manaea went 11-10 with a 3.91 ERA in 32 starts last year. He had two shutouts and struck out a career-high 194 batters, ranking eighth in the American League.
The addition of Manaea could lead to another move for San Diego, which was already flush with starting pitching before the trade with Oakland.
The A's are rebuilding after going 86-76 last year, missing the playoffs for the first time since 2017. Right-hander Chris Bassitt, slugging first baseman Matt Olson and third baseman Matt Chapman were traded last month.
Martinez played for Double-A San Antonio and Triple-A El Paso last year, going 8-5 with a 3.38 ERA in 26 games, 22 starts. The right-hander finished with 122 strikeouts in 125 innings.
Martinez, 25, missed the 2016 season following Tommy John surgery and the 2020 season because of the pandemic.
Angeles played for Low-A Lake Elsinore and High-A Fort Wayne last year, batting .329 with four homers, 64 RBIs and 19 stolen bases in 105 games. The 19-year-old right-handed hitter was signed by the Padres out of the Dominican Republic in 2018.
Manaea was selected by Kansas City in the first round of the 2013 amateur draft. He was traded to Oakland in the July 2015 deal that moved Ben Zobrist to the Royals.
Manaea is 50-41 with a 3.86 ERA and 641 strikeouts in 129 career games, including 128 starts, in six seasons. He agreed to a $9.75 million, one-year contract last month, avoiding arbitration.
Holiday, 21, was selected by Oakland in the 13th round of the 2021 amateur draft. He went 2-0 with a 0.00 ERA in three relief appearances with the A's affiliate in the Arizona Complex League last year.