The four-time All-Star missed last season while recovering from elbow surgery on his throwing arm, but the 31-year-old Sheets said he is confident he will quickly return to form.
"I am pretty sure when I get back up there that all my instincts that I have learned in the past is going to come back so I am not really that nervous," Sheets told a news conference. "I feel renewed for the game and I am really keen to get back out there and compete."
Oakland did not disclose financial terms of the deal but said it expects Sheets will be a leader on the team's young pitching staff that ended last season with the third-best ERA in the American League.
Sheets, who spent his first eight major league seasons with the Milwaukee Brewers, went 13-9 with a .309 ERA during 31 starts with Milwaukee in 2008 before having an operation last February on the elbow of his throwing arm.
Oakland went 75-87 last season and finished last in the American League's West Division.
(Writing by Frank Pingue in Toronto; Editing by Justin Palmer)