The pair, signed to minor league contracts as free agents, would have been able to opt out of their deals if they hadn't been told by Tuesday they will be added to the 40-man roster.
Sanchez will move into the No. 4 spot in the rotation. That job opened over the weekend, when right-hander Jeff Karstens was bothered by a sore shoulder. The 30-year-old Sanchez was 1-9 with an 8.07 ERA last season for Kansas City and Colorado. He pitched a no-hitter in 2009 for San Francisco.
"In spring training, he's looked much closer to the guy he was in 2011 and '10 than the guy who struggled in '12," general manager Neal Huntington said. "Jonathan's last two starts have been very encouraging. The offspeed pitches have been very effective and the fastball command has been good."
Inge, who is bothered by a bone bruise in his right shoulder, might open the season on the disabled list. Inge has played in only four games since being hit by a pitch in a game March 14.
Sanchez gets a one-year deal worth $1.375 million and Inge a deal for $1.25 million. The pair must be put on the 40-man roster by Sunday.