Haren is 7-8 this season with a 4.60 earned run average. The three-times All-Star has averaged 15 wins a season over the last four years.
"We really felt good about our starting five moving forward, but this is a huge opportunity for us to upgrade," Angels manager Mike Scioscia told reporters.
"Not only now but the next couple years. He's definitely a guy who's pitched in big games. He has his stuff and is a young veteran. It gives us a deeper front of the rotation. That's what every championship-caliber team strives to do."
In eight seasons with St. Louis, Oakland and Arizona, Haren is 86-70 with a 3.71 ERA.
"I did have some good years here, this year hasn't been that great personally but I was brought here to put us over the top," he said. "It didn't happen that way unfortunately."
Saunders, an All-Star in 2008 and the Angels second starter in their rotation, was 6-10 this season with a career high 4.62 ERA.
Rodriguez, 25, is a right-handed relief pitcher with Triple-A Salt Lake and has 10 saves this season. Twenty-one-year-old Corbin is a left-handed starter and is 13-3 in 20 starts in Single-A.
(Reporting by Mike Mouat in Windsor, Ontario. Editing by Ian Ransom)