The Padres have reached agreement on a minor league deal with lefty Matt Thornton, according to Ken Rosenthal of FOX Sports (via Twitter). He is undergoing a physical today and will join the team in major league camp if he passes.

The deal will pay Thornton at a $1.6MM base salary if he can crack the MLB roster, Chris Cotillo of SB Nation tweets. It also includes $1.9MM in available incentives relating to his number of appearances.

Thornton, 39, saw his strikeout rate fall last year but continued to post excellent results while being tasked with a fairly light workload. Though he’s now within eyesight of 40, the southpaw owns a 1.98 ERA over 77 1/3 innings over the prior two seasons.

While he’s been particularly stingy against lefties, Thornton has also posted solid numbers (sub-.700 OPS against) in his exposure to right-handed pitching in that span. He’s finally experienced a bit of a downtick in velocity, but still brought his average heater at around 93.5 mph last year.