OAKLAND -- More sighs from the Oakland faithful were likely heard this week, when free-agent outfielder Josh Willingham officially signed with a team not named the A's.

Willingham, who agreed to a three-year deal with the Twins for $21 million -- he'll make $1 million more per season than he did with the A's this year -- represents the second of Oakland's free agents to depart the Bay Area, as David DeJesus joined the Cubs a couple of weeks ago.

Fellow outfielder Coco Crisp is likely to follow, leaving the outfield a top priority for an A's team that's suddenly staring down a rebuild. It's not so much a friendly scene for fans right now, nor was it the preferential path in the eyes of Willingham, who on Friday said he hoped to stay in Oakland if awarded a long-term contract.

Such a deal was discussed in August and September, Willingham said, but increasingly became less of a reality at season's end.

"Talks of an extension were there for a while," Willingham told MLB.com by phone from his Alabama home. "But I can say [A's general manager] Billy Beane's always been real honest with me, and he didn't know what they were going to do, so he pretty much told me they were going to offer me a one-year arbitration contract and that was probably going to be it."

They did, and as a result of Willingham's signing with the Twins, will get a supplemental pick after the first round of next year's First-Year Player Draft as compensation, as well as a pick in front of Minnesota high in the second round. Normally the latter would come in front of the first-round pick, but the first 15 picks are protected and the Twins are slated to choose second overall.

Willingham noted there were four teams "seriously interested" in his services at the time of his decision. The A's, obviously, weren't included in that mix, but Minnesota proved quite the attractive landing spot for the outfielder, who last year compiled a career-high 29 home runs and 98 RBIs.

"Having a three-year deal, that was big for me," he said. "And you look at a lot of other factors, as well. It's in the Midwest, so it's closer to home and will be easier on family. You look at the organization, and I've talked with plenty of players who have played there, and there wasn't a bad thing said about it. All of that kind of plays into a decision."

Still, he feels for the teammates he leaves behind in Oakland, where there remains plenty of questions about the future. Right-hander Trevor Cahill and lefty Craig Breslow have already been dealt, and Gio Gonzalez and Andrew Bailey could be traded shortly, as well -- all for prospects the A's hope will field a new stadium that's yet to garner approval.