Dan Haren

Former Angels starting pitcher Dan Haren has agreed to a one-year contract with the Dodgers. (Jae C. Hong / Associated Press / June 22, 2012)

The Dodgers are close to signing former All-Star Dan Haren, who could add depth to the battered back end of their rotation.

Haren agreed to a one-year, $10-million contract that includes a vesting option for 2015, according to people familiar with the situation who spoke under the condition of anonymity because the deal is pending a physical examination. The contract could be finalized as early as Monday.

Haren is coming off the two worst seasons of his career. He was 12-13 with a 4.33 earned-run average with the Angels in 2012 and 10-14 with a 4.67 ERA with the Washington Nationals this year.

But Haren pitched well over the last three months of the season, posting a 3.32 ERA over his last 15 starts, and offers the Dodgers some protection without a long-term commitment.

Haren figures to pitch somewhere behind Clayton Kershaw, Zack Greinke and Hyun-Jin Ryu. The team's two back-end starters, Chad Billingsley and Josh Beckett, are recovering from operations.

Billingsley, who had reconstructive elbow surgery, isn't expected back until at least May. Beckett faces an even more uncertain future after an operation for a nerve problem.

Pitching depth could be important for the Dodgers if they fail to land, or decide not to seriously pursue, Masahiro Tanaka of Japan. Tanaka might not be available this off-season because there isn't an agreement in place on how non-free-agent Japanese players can move to the United States. Even if Tanaka is auctioned by the Tohoku Rakuten Golden Eagles, there's no guarantee the Dodgers will secure his rights.

The Dodgers were interested in re-signing Ricky Nolasco, but not to the four-year deal he is seeking.

Because Haren didn't receive a qualifying offer from the Nationals — essentially, an offer for a one-year, $14.1-million contract — the Dodgers won't forfeit their top pick in the draft if their deal with him is finalized.

Haren was considered a top-tier starter from 2005 to 2011, which he split between the Oakland Athletics, Arizona Diamondbacks and Angels. Over those seven seasons, he was a combined 101-74 with a 3.49 ERA.

Haren grew up in Southern California, pitching at Bishop Amat High in La Puente and Pepperdine. He makes his offseason home in Orange County.

dylan.hernandez@latimes.com

Twitter: @dylanohernandez