Chen, 29, was 16-6 with a 3.54 ERA in 31 starts, setting a career best for wins. He had 54 starts in the past two seasons, two shy of the amount needed for his 2015 salary to become guaranteed at $6 million.
O'Day, 32, was 5-2 with four saves and a career-low 1.70 ERA in 68 games.
If the options had been declined, O'Day would have received a $400,000 buyout and Chen $372,000.
The moves were announced Thursday.