Atlanta released Thornburg on Sunday.
Thornburg likely chose not to accept an outright assignment to Triple-A Gwinnett after he cleared waivers earlier in the weekend, so he'll pursue work with another organization after a two-month stint with Atlanta. Before being designated for assignment, Thornburg made nine appearances out of the big-league bullpen and gave up four earned runs on 12 hits and five walks while striking out 10 over 9.1 innings.