A nine-year veteran, Santana already had received one-year offers from the Baltimore Orioles and Toronto Blue Jays along with a three-year offer from the Minnesota Twins, a source confirmed to ESPNdeportes' Enrique Rojas.
"It was a lot of waiting, but thank God I already have a team to play. Can't wait to play," Santana told ESPNdeportes.com.
"It was hard. I had a lot of patience, but my family and God are always right next to me, and that helped me."
Santana, 33, went 9-10 with a 3.24 ERA in 32 starts for the Kansas City Royals last season and should make an immediate impact with the battered Braves, who are facing the prospect of opening the season with Kris Medlen, Brandon Beachy and Mike Minor on the disabled list.
"In light of what has happened over the past few days with our pitching staff, we felt it was incumbent on us to do everything we could to strengthen our starting pitching," Braves general manager Frank Wren told reporters before a game against Washington.
Santana threw a bullpen at the Braves spring training complex on Wednesday, which manager Fredi Gonzalez said went well. Despite his late entrance to camp, Santana could be ready for the start of the season.
Medlen, who had been named Atlanta's Opening Day starter, left a spring training start on Sunday after grabbing his right elbow. Initial tests showed ligament damage, and he is undergoing further examination to determine whether he needs surgery for the second time in less than four years.
Beachy left a start Monday because of continuing problems with his right elbow, and Minor has yet to pitch this spring because of a sore shoulder.
Santana will be pitching in the National League for the first time in his 10-year career.
"I've played my whole career in the American League, but I wanted to explore something different, to see how it goes," Santana told ESPNdeportes. "Batting doesn't scares me; I was a batter as a kid."
Blue Jays general manager Alex Anthopoulos told Sportsnet 590 The FAN on Wednesday that he was told Santana wanted to pitch in the NL.
"From what I was told we couldn't compete with the NL," Anthopoulos told The FAN, according to Sportsnet. "The NL was where he wanted to be. It was not money, it was not years."
Santana spent eight seasons with the Los Angeles Angels before being traded to the Royals in 2013, helping Kansas City post an 86-76 record, its best since 1989.
But Santana, who made $13 million in the final year of his contract, turned down a $14.1 million qualifying offer from the Royals and became a free agent. Given his hefty contract demands, he remained unsigned as spring training began despite putting up some impressive career numbers.
Santana was an AL All-Star in 2008, tossed a no-hitter in 2011 and has reached double-figure wins five times, going a career-best 17-10 in 2010 and twice winning 16 games.
Overall, he is 105-90 with a 4.19 ERA.
While the Braves said they have not yet determined the extent of Medlen's injury, Wren acknowledged the outlook is "worrisome." Medlen went a team-leading 15-12 with a 3.11 ERA last season.
Beachy underwent elbow surgery in 2012 and has been limited to a total of 18 starts over the past two seasons, enduring several setbacks in his attempt to come back. After his latest problem, he will miss his next scheduled spring start and faces another trip to the DL.
Minor, who underwent urinary tract surgery on Dec. 31, hopes to pitch within the next week but also seems likely to start the season on the DL while he builds his arm strength. The left-hander was 13-9 with a 3.21 ERA in 2013.
With Opening Day less than three weeks away, the only healthy members of the Braves' projected rotation are second-year pitchers Julio Teheran (14-8 last season) and Alex Wood, rookie David Hale and non-roster invitee Freddy Garcia. Atlanta also signed veteran Gavin Floyd, but he is coming off Tommy John surgery and won't be ready to pitch until at least May.
Now, add Santana to the list, although it's not known how long it will take to get his arm ready for the rigors of the regular season.
By signing Santana, the Braves forfeited their first-round pick in June's amateur draft, No. 26 overall, and the Royals will receive a compensation-round selection, the 28th overall. Atlanta's first pick is now 32nd overall, as compensation for losing free agent catcher Brian McCann, who signed with the New York Yankees.
Santana's signing leaves only two free agents -- Stephen Drew and Kendrys Morales -- available from the 13 players who turned down qualifying offers. If they agree to one-year contracts after opening day, they wouldn't be subject to qualifying offers this November. If they wait until after the draft to reach agreements, clubs that sign them won't lose selections.
Among the 22 qualifying offers in the two years of the new labor contract, none have been accepted.
"Frankly, the players haven't adjusted to the change," New York Mets general manager Sandy Alderson said. "To blame the system versus the marketplace and blame the system versus a misunderstanding of the marketplace I think is a little one-sided. From a management standpoint, I'd say, `Hey, I'm surprised if you guys haven't taken a qualifying offer.' Maybe they should have."
The Associated Press contributed to this report.