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The Brewers have added veteran right-hander Kyle Lohse to the fold. (Getty Images)

CBSSports.com's Jon Heyman reports that free-agent right-hander Kyle Lohse has agreed to a deal with the Brewers, pending a physical. Heyman adds that Lohse is right now en route to Brewers camp for his pre-signing examination. Tom Haudricourt of the Milwaukee Journal Sentinal puts the deal at $33 million over the three years. CBSSports.com's Danny Knobler confirms those parameters.

The 34-year-old Lohse remains available despite a 2012 season in which he posted a 2.86 ERA, 1.09 WHIP and 3.76 K/BB ratio across 211 innings for the Cadinals and finished seventh in the NL Cy Young balloting. The 2012 campaign was easily Lohse's best ever, and the question moving forward is whether he can approximate that performance again in 2013 and beyond. For his career, the 12-year veteran has a record of 118-109 and an ERA+ of 97.

Lohse figures to slot in behind ace Yovani Gallardo in the Milwaukee rotation.

While Lohse has been keeping himself fit this offseason, he figures to need some time to round into regular-season shape. As such, it's not yet certain when he'll be able to join the Brewers' starting five.

Because the Cardinals tendered Lohse a qualifying offer this winter, the Brewers, should the signing be finalized, will forfeit the 17th-overall pick of the June draft and the slot money attached to that pick. The Cardinals, in turn, will receive an additional compensatory draft choice -- the 28th-overall pick, in this instance.