It is a split contract, which would pay him $700,000 if he remains in the major leagues all season.
He is scheduled to report to Sarasota on Wednesday, the source said.
Willis, 30, was released by the Phillies last week. He had signed a one-year, $1 million deal with Philadelphia in December. He was auditioning for a bullpen spot this spring, allowing five runs in 2 2/3 innings and recording a 16.87 ERA in three appearances, walking four and striking out none before being released on Friday.
Willis, once the top young left-hander in baseball, has played for four major league team in his nine-year career, including the Marlins,when he won the National League Rookie of the Year in 2003 and finished second for the National League Cy Young Award voting in 2005 when he was 22-10 with a 2.63 ERA.
Last year with the Reds, he was 1-6 with a 5.00 ERA in 13 starts. He has not had a sub-5.00 ERA in a big-league season since 2006 and he has won just five major league games in his last four seasons.
The Orioles' signing of Willis was first reported by ESPN.com.Copyright © 2015, The Baltimore Sun