The deals, which will be announced by the Twins once the players officially sign, include invitations to Major League Spring Training. Both pitchers made starts for the Twins in 2012 after signing Minor League deals before the season.
Deduno, 29, elected to remain with the Twins after he was outrighted to Triple-A Rochester on Friday and taken off the 40-man roster.
The right-hander struggled with his control but was a pleasant surprise for the Twins last season, posting a 4.44 ERA in 15 starts. He struck out 57, walked 53 and gave up 10 homers in 79 innings.
He earned his spot in the rotation in the second half of the year after he had a 2.14 ERA with 46 strikeouts and 22 walks in 42 innings with Triple-A Rochester.
Deduno, though, saw his season cut short in the last week of the season because of inflammation in his left eye, but the injury didn't turn out to be serious.
Vasquez, meanwhile, didn't fare as well in his time with the Twins, as he had a 5.68 ERA in six starts with 14 strikeouts and 19 walks in 31 2/3 innings. But the 29-year-old fared much better in Triple-A with a 2.78 ERA and 98 strikeouts and 39 walks in 100 1/3 innings.
It was his first year starting since 2008, after he spent the previous three seasons as a reliever in the D-backs' organization.
Both pitchers will give the Twins some depth at the back end of their rotation. Left-hander Scott Diamond remains the only pitcher guaranteed a rotation spot next season.