The signing comes one day before Grieve would have been forced to return to the Athletics for the minimum major league salary for second-year players. He earned $172,000 last season.
A's general manager Billy Beane met Tuesday with Grieve's agent, Alan Hendricks. The team hopes to get a multiyear contract completed later this year.
"We've preserved that opportunity. We still haven't accomplished what we set out to do," Beane said. "This just takes the focus off the player's contract."
The A's had hoped for a multiyear contract before the start of the season. But Todd Helton's $12 million, four-year contract with Colorado last week upped Grieve's price, according to Beane.
"We had a much better chance a week or 10 days ago," Beane said. "The Todd Helton contract torpedoed a lot of multiyear deals that were being discussed."
Grieve said he wasn't too concerned with getting a long-term deal before the season.
"I would like to if it is the right deal," he said. "I wouldn't want to if it wasn't."
Grieve, the son of former major-league outfielder and executive Tom Grieve, was the only player named on all 28 ballots in the AL Rookie of the Year voting.
The 22-year-old hit .288 with 18 homers and 89 RBI last season for the Athletics, who finished in last place in the AL West at 74-88. Oakland also began committing to the future with players such as Grieve, 23-year-old catcher A.J. Hinch and 24-year-old outfielder Ryan Christenson.
Grieve hit over .300 in each of the first three months of the season, highlighted by a .340 average in June, when he had five homers and 18 RBI. He completed June with 12 homers and 51 RBI.
He tired toward the end of the season, hitting no better than .257 in any of the last three months while collecting six homers and 38 RBI.
Grieve was the fifth AL Rookie of the Year in franchise history and the first since shortstop Walt Weiss in 1988. Jose Canseco and Mark McGwire won the award in 1986 and 1987, respectively. Philadelphia Athletics pitcher Harry Byrd captured the honor in 1952.
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