San Diego got Manaea, 30, 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 Padres' rotation features Opening Day starter Yu Darvish, Joe Musgrove, Blake Snell and Nick Martinez. Right-hander Chris Paddack is on the injured list with an oblique injury while fellow righty Mike Clevinger will begin the year on IL as he continues to recover from Tommy John surgery.
Hours after the trade was announced, Manaea made his first start for the Padres -- against the A's. He had been scheduled to pitch Sunday, so he put on a new Padres uniform and took on the Athletics, giving up one run and six hits in 3⅔ innings.
Still wearing a green glove, Manaea smiled as he faced his former teammates, and visited with them from outside the Oakland dugout.
"I was thinking of having him pitch in an A's uniform with a Padres hat," said San Diego manager Bob Melvin, who was Oakland's manager prior to this season.
The A's are rebuilding after going 86-76 last year, missing the playoffs for the first time since 2017. Oakland has sent first baseman Matt Olson to Atlanta, third baseman Matt Chapman to Toronto and right-hander Chris Bassitt to the Mets this offseason.
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 Athletics' affiliate in the Arizona Complex League last year.
The Associated Press contributed to this report.