Inge joined the team in Boston on Monday and the team designed Luke Hughes for assignment to make room for Inge.
Inge, 34, was hitting just .100/.100/.300 with two hits in 20 at-bats for the Tigers this season, with both of his hits going for extra bases with a homer and a double. He hit .197/.265/.283 last season and is a career .234/.304/.387 hitter in parts of 12 seasons, all with the Tigers.
"It's a little different, I'm not going to lie, looking down at these white shoes," Inge told reporters, including MLB.com's Jane Lee (via Twitter).
According to Susan Slusser of the San Francisco Chronicle, Inge will make the pro-rated major-league minimum. Inge is still scheduled to make $6 million from the Tigers ($5,500,000 for 2012 and a $500,000 buyout for 2013).
Inge's impact on Oakland's offense could be minimal, but he's an immediate defensive upgrade for a team whose third basemen (Hughes, Josh Donaldson and Eric Sogard) have combined for eight errors so far this season.
Hughes had been picked up off waivers from the Twins earlier this season and was hitting just .130/.125/.130 in eight games between the Twins and A's. He had just one hit in 13 plate appearances for Oakland. He had three errors in four games with the A's.