The deal, according to a baseball source, is worth $3 million and includes potential performance bonuses.
"One of the reasons I think we won a lot last year was because of the depth in our rotation, and we've still got such a young staff," said general manager Billy Beane. "Bart was so good for us last year, and given the cost of those type of players, we thought it was the best thing for us next year."
This is despite Colon's early departure from the 2012 campaign because of a 50-game drug suspension, after he posted a 10-9 record and 3.43 ERA in 24 starts for the A's. He still has five games remaining on his ban.
"When he serves his suspension, he'll have paid his dues as laid down by the labor agreement," said Beane.
Colon's 10 victories during the 2012 campaign were his most since 2005, when he tallied 21 en route to capturing the American League Cy Young Award while pitching for the Angels.
He joins a pitching staff that already includes Brett Anderson, Jarrod Parker, Tommy Milone, A.J. Griffin and Dan Straily. Travis Blackley and Minor Leaguers Brad Peacock and Sonny Gray are also options.
"We liked the way he pitched on the field," said Beane. "We liked his performance on the field. His on-the-field performance is the reason for this decision. I think he showed how beneficial throwing strikes are. I think that was the best influence he could have had on our young guys."
Colon, 39, is currently pitching in the Dominican Winter League. He has compiled a 1-0 mark and 2.89 ERA in two outings.
Colon's signing, Beane said, will not have an impact on the potential return of free agent Brandon McCarthy, whom the A's are still interested in bringing back.