Green was first drafted by the Houston Astros in the 11th round (329th overall) of the 2003 Major League Baseball draft, after his freshman season at Darton College in Albany, Georgia. However, he did not sign and was later taken by the Anaheim Angels in the 35th round (1,043rd overall) of the 2004 draft.
After signing with the Angels, he played with the Rookie League Provo Angels in 2004. Making 10 starts and 7 relief appearances, he went 4–3 with a 4.03 ERA. In 2005, while playing for the Class A Cedar Rapids Kernels, Green made 8 starts and 18 relief appearances. He went 3–3 with a 3.58 ERA.
He split the 2006 season between the Class A-Advanced Rancho Cucamonga Quakes and the Double-A Arkansas Travelers. He made a combined 28 starts and went 13–8 with a 4.32 ERA. His 177 innings pitched were a career high for him, and so were his 13 wins, 28 starts, and 134 strikeouts.
Green pitched for the Travelers again in 2007, making 28 starts and compiling a 10–8 record with a 3.68 ERA, a career high. He also pitched a career high 2 complete games and 178⅓ innings. On November 2, his contract was purchased by the Angels, protecting him from the Rule 5 draft. He spent the entire 2008 season with the Triple-A Salt Lake Bees.