The 33-year-old Francis was claimed off waivers by the A's from Cincinnati on May 18 and went 0-1 with his first career save and a 6.08 ERA in nine relief appearances with Oakland.
He was designated for assignment July 3 when Eric O'Flaherty was reinstated from the disabled list.
Francis is 0-2 with a 5.89 ERA in 10 games this season and 70-80 with a 4.95 ERA in his career with Colorado, Kansas City, Cincinnati and Oakland.
Yankees manager Joe Girardi said Francis most likely will be used out of the bullpen initially but could eventually see time as a starter. He had not yet arrived in Baltimore prior to Friday's game against the Orioles.