Santana, who turns 35 later this month, will be available to the media at his locker Wednesday morning and will work out at the Ed Smith Stadium complex.
The two-time Cy Young Award winner is recovering from a second surgery to repair his left shoulder capsule. He's 139-78 with a 3.20 ERA in 12 major league seasons.
Most recently, Santana went 6-9 with a 4.85 ERA and two complete games in 21 starts with the Mets in 2012.
Santana, who was acquired by the Twins via the Marlins in the 1999 Rule 5 Draft, will wear No. 57. Outfielder Francisco Peguero will need a new number.
The Orioles were among seven teams that watched Santana throw last week. A report in the New York Post stated that his fastball sat at 77-78 mph and topped out at 81.
It's possible that the Orioles could use Santana out of the bullpen as an extra left-handed reliever if he's healthy and regains more velocity on his fastball.
Santana posted a 2.93 ERA in five career playoff starts from 2003-06. He also made three scoreless All-Star Game appearances over three innings. He's the second-winningest Venezuelan-born pitcher in baseball history behind Freddy Garcia (156) and 12 strikeouts shy of 2,000 for his career.
From 2004-08, Santana worked 228, 231 2/3, 233 2/3, 219 and 234 1/3 innings and posted ERAs of 2.61, 2.87, 2.77, 3.33 and 2.53. He also was idolized back in Venezuela by current Orioles minor league pitcher Eduardo Rodriguez, who posted a photo with Santana yesterday on his Instragram account.
"When I was young, my father every time would tell me about him," said Rodriguez, 20, who's emerged as one of the top pitching prospects in the organization. "He'd say, 'Hey, he's the best player in baseball. He's the best player from Venezuela.' He was my favorite player for all my life.
"When I saw him here, I go (wipes eyes). I talked to him and I told him, 'When I was young, my father told me that you were the best and you were my favorite player.' He said, 'Oh, I'm excited about that. Thank you.'
"It's a great opportunity with the Orioles and a great opportunity for me. He can tell me about his pitches, like how to throw his changeup in situations. That's good for me. He can help me. You know what I mean?"
Shortstop J.J. Hardy also understands the off-field benefits of having Santana in the organization.
"I don't know what the terms are or anything, but if he's anything like what he used to be, he's going to help," Hardy said. "He's a pitcher with a lot of experience, great reputation from everyone I've talked to who's played with them. They say he's an awesome guy, a great clubhouse guy. There are a lot of things you can take from it, all of them positive.
"With all the young pitchers we have, they can pick his brain a little bit. Even when he wasn't at his best when he was in New York and he was hurt, he was still pretty nasty, striking out about a guy an inning. If he gets back to what he can do, then sure, he's definitely going to be able to help."
Santana will receive $3 million, plus performance bonuses, according to CBSSports.com.
Per the New York Post, Santana's deal includes $5.05 million in available bonuses and a May 30 opt-out date.