The Warriors’ newest addition, forward Jonas Jerebko, has a lengthy offseason to-do list: find a Bay Area home, move, stay in playing shape and, of course, begin getting to know his new teammates.

One of the first players he plans to call is DeMarcus Cousins, who signed a one-year, $5.3 million deal with Golden State this month after a recent Achilles injury severely limited his market value in free agency. Jerebko, who missed the 2010-11 season with an Achilles injury, wants to help Cousins through the recovery process.

“I’m definitely going to talk to him when I get the chance,” Jerebko said during his introductory media availability Monday at the Warriors’ practice facility. “He just needs to take his time. He’s going to be back, no problem.”

Drafted by Detroit at No. 39 overall in the 2009 draft, Jerebko — the league’s first Swedish-born player — was a bit of a revelation as a rookie, averaging 9.3 points, 6 rebounds and one steal in 27.9 minutes per game. Then, in the first quarter of a preseason loss to the Heat on Oct. 5, 2010, he fell hard in the lane and strained his right Achilles tendon.

Over the next 14 months, Jerebko labored through a rigorous rehab regime and was forced to watch games from the bench. After showing the Pistons’ staff that he was healthy enough to return to the court, Jerebko signed a four-year contract in December 2011 and resuscitated his career.

“It was tough, but there was no stopping there,” Jerebko said of missing a full season because of injury. “I had to get back to work and try to earn a new contract, and I did. It was a tough time, but it’s behind me now. It was a long year.”

Now entering his ninth NBA season, Jerebko has yet to match his rookie season’s production. The pain from that Achilles injury has long subsided, however, and he comes to the Warriors as a proven three-point shooter off the bench.

Now Playing:

Jerebko hopes that Cousins will benefit from hearing his story. When he ruptured his left Achilles tendon 48 games into last season while playing for New Orleans, Cousins was averaging 25.2 points, 12.9 rebounds and 5.4 assists. Cousins, who had surgery Jan 31, joined Golden State in part because the defending NBA champion won’t rush him back into the lineup.

With four other All-Stars in their prime, the Warriors have the luxury of giving Cousins the bulk of the regular season to recover from his injury. There is a chance that he could return as early as December. However, Golden State hopes simply that he is back for the playoffs.

“I took my time,” Jerebko said of his recovery process from his Achilles injury. “It took quite some time, but I did my rehab right and I know he’s going to be back 100 percent.”

Connor Letourneau is a San Francisco Chronicle staff writer. Email: cletourneau@sfchronicle.com Twitter: @Con_Chron