The 26-year-old outfielder is set to make $36 million during that time, MLB.com confirmed.
The deal, which won't be officially announced by the A's until Cespedes has taken a physical, precludes Oakland from offering him arbitration, meaning the outfielder will automatically become a free agent at the conclusion of the 2015 season.
"I am super happy because it's been a dream of mine for a long time," Cespedes told MLB.com from the Dominican Republic. "To leave my country and play in the big leagues is what the goal was. My family is really happy, too. They are living their dreams through me."
Oakland is believed to have outbid the Miami Marlins, who had been considered the favorites to land Cespedes amid a competition that also included the Cubs, Tigers, Orioles and White Sox. Just last week, Cespedes was in Miami via a travel visa, touring the Marlins' new facility with agent Adam Katz.
"Miami was a great visit," Cespedes said. "I had a good time. I ate with the team president and other people in the front office. They were nice and it was a great experience, but the A's were for me.
"It was a great process, training and working out for teams. It was a difficult decision to leave Cuba, but I'm really excited with how things worked out. I saw a bunch of teams and they saw me, too, but Oakland was the best for me."
The Marlins reportedly offered Cespedes a six-year deal ranging in value from $36 million to $40 million but were not willing to give him $9 million per year, as the A's did.
Moreover, Cespedes' representatives felt "the A's wanted him more than anyone else," MLB.com's Peter Gammons reported via Twitter. Oakland was among the finalists for Cuban players Aroldis Chapman and Alexei Ramirez when they were free agents after defecting in recent years.
By snagging Cespedes, thought to be a five-tool player, Oakland has landed a power-hitting center fielder who will perfectly slot into the middle of what was previously a lackluster lineup. He can play all outfield positions but is best suited for center, meaning Coco Crisp could potentially settle at one of the corners.
The A's, who essentially entered the offseason with a blank outfield, also have Josh Reddick, Seth Smith, Collin Cowgill and Jonny Gomes in the mix -- a scene that should make for an eventful Spring Training.
"My first goal is to make the team and stay healthy all season, and little by little, I'll make more goals," Cespedes said. "I've been preparing every day for this, and I 100 percent believe that I am ready for the Major Leagues. I have a lot of international experience and experience at a high level. I'm very confident in my abilities.
"Believe me, I'm going to give the best I have, and I'm going to leave it all on the field. I'll do my best and show I deserve this opportunity. I know I can do it. I'm ready."
Monday's move also perhaps restores faith in doubtful fans who, earlier in the winter, watched Oakland trade All-Star pitchers Trevor Cahill, Gio Gonzalez and Andrew Bailey as it looks ahead to the potential of moving into a new stadium in San Jose. Cespedes' signing would seem to complement the A's plans of contending in that new home, although there's no guarantee he'll still be with the A's when that time comes.
The 6-foot, 215-pound Cespedes played eight seasons for Granma in the Cuban League, tallying a record 33 home runs to go along with a .333 average and 99 RBIs in 90 games during the 2010-11 campaign. He was also Cuba's starting center fielder during the 2009 World Baseball Classic, batting .458 in six games.
The Cuban defector, who recently gained temporary residence in the Dominican Republic, was declared a free agent by Major League Baseball on Jan. 25 but was not allowed to sign with a team until legally cleared by the U.S. Treasury Department's Office of Foreign Assets Control.
Recently unblocked, Cespedes was free to sign with the A's, and he'll need to obtain a worker's visa before joining the team in Arizona for Spring Training.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. Jesse Sanchez contributed reporting. This story was not subject to the approval of Major League Baseball or its clubs.