Norris, 30, was designated for assignment by the Orioles in July and later cleared waivers on Aug. 10. He was part of their Opening Day rotation.
The Padres will pay only the pro-rated part of the Major League minimum salary for Norris, approximately $150,000.
"He's a guy that's started, has had a lot of starting success over the last few years. From our standpoint, obviously it was a difficult year in Baltimore. It was a chance to bring him in here in maybe a little different role," said Padres general manager A.J. Preller.
"He's a talent. [We] wanted to bring him in here and see what he does over the next several weeks."
Norris had a 7.06 ERA in 18 games -- including 11 starts -- for the Orioles. He spent three weeks on the disabled list in May and early June with bronchitis, which he said took a toll on him physically.
"We still didn't know how to diagnose it exactly, but they called it bronchitis at the time," said Norris, who lost 17 pounds when he was sick. "I'm still kind of battling it a little bit. My immune system didn't like it or take to it too much but feeling a lot better."
The Padres plan on using Norris, who hasn't appeared in a game since July 30, in one-inning stints for the time being, said interim manager Pat Murphy.
Norris was coming off a strong 2014 season when he posted a career-high 15 wins along with a 3.65 ERA last year. He went 8-2 with a 3.27 ERA in 13 second-half starts, helping the Orioles win the AL East.
"I had an amazing run with Baltimore last year, but got sick and battled some things," said Norris, who is a California native. "... But honestly to get another opportunity to play this game that I love here in San Diego, on the West Coast, near my family -- it's truly a blessing in disguise.
"I'm just excited to be here, want to do my part and help these guys. Anything can happen in the last two months."
Norris, who was making $8.8 million with the Orioles, will be a free agent after the season. This could essentially amount to an audition for next year.
"From our standpoint, it's a chance over the next six weeks to put him in this role and see how he does," Preller said. "And at that point, we'll re-evaluate."