Ramirez is expected to report to spring training by Friday.
The deal is worth about $500,000. Ramirez is obligated to serve a 50-game suspension without pay before beginning play for the A's due to violating baseball's drug policy for the second time. With no rainouts, the first game Ramirez would be eligible to play is on his 40th birthday -- May 30 at Minnesota. That didn't deter general manager Billy Beane and the Athletics.
"I am very pleased Billy was able to add Manny to our team," A's owner Lew Wolff said in an email. "I look forward to welcoming him and the entire team that Billy and his people have assembled for the coming season."
The A's recently agreed to terms on a $36 million, four-year contract with highly sought-after outfielder Yoenis Cespedes, a Cuban defector who has expressed interest in playing with Ramirez.
At baseball's winter meetings in December, it was announced that Ramirez had applied for reinstatement. He had his suspension for a second failed drug test cut to 50 games because he sat out nearly all of last season.
MLB had announced his retirement April 8, saying he was notified "of an issue" under the drug program.
Ramirez ranks 14th on the career list with 555 home runs. He went 1-for-17 (.059) in five games last season for Tampa Bay, which had signed him to a one-year deal worth $2.02 million.
This would be the 20th major league season for Ramirez, a career .312 hitter with 1,831 RBIs. Oakland, which traded away its top three pitchers this offseason including two starters, could use a power bat in the middle of the order in a tough AL West that already has seen the key additions of Albert Pujols on the Los Angeles Angels and star Japanese pitcher Yu Darvish for the two-time reigning AL champion Texas Rangers.
The A's haven't reached the playoffs or had a winning season since being swept by the Tigers in the 2006 American League Championship Series.
Information from The Associated Press was used in this report.