Hale, 27, spent all of last season with the Braves, and he went 4-5 with a 3.30 ERA in 45 games (six starts). Schlosser, 26, went 0-1 with a 7.64 ERA in 15 relief appearances for the Braves, and he was 7-6 with a 4.17 ERA in 25 games (15 starts) at Triple-A Gwinnett.
They could compete for a starting spot in a rotation that is led by lefty Jorge De La Rosa and righty Jhoulys Chacin and also includes a pair of 24-year-olds who had their moments last season -- righty Jordan Lyles and lefty Tyler Matzek. Hale and Schlosser also could work out of the bullpen.
"The fact that both guys have started in the past was an appealing part of who they are, and their history," Rockies general manager Jeff Bridich said.
Bridich said the Rockies will continue to look at trades or the free-agent market for established pitching. Reports surfaced of a possible deal with the Mets for righty Dillon Gee, but the teams have not agreed upon a package. The Rockies also have been linked to veteran free agents such as Kyle Kendrick and Paul Maholm. The club has also considered several veteran relievers on the market.
Hale, who was selected by the Braves out of Princeton in the third round of the 2009 First-Year Player Draft and entered last year as Atlanta's No. 7 prospect, is potentially under club control through 2019. Schlosser, a 17th-round pick out of Florida Southern in 2011, has less than a year of Major League service time.
Hale has made one appearance at Coors Field. He earned the win by giving up one run and two hits in 2 1/3 innings of the Braves' 13-10 victory over the Rockies on June 10, 2014. Hale throws from a conventional three-quarters delivery, while Schlosser throws sidearm, but the two pitchers are otherwise similar.
"Neither guy has reached his fullest potential," Bridich said. "The ability to, in both guys, get ground balls and the fact they do that well and naturally is part of the equation."
The Rockies designated left-hander Jayson Aquino for assignment to make room on the 40-man Major League roster for Hale. Aquino, 22, was invited to Major League camp last year and was hit in the head with a line drive during an intrasquad game but not seriously hurt. During the season, he went 5-10 with a 5.13 ERA in 18 starts, 16 at Class A Advanced Modesto and two at Double-A Tulsa.
The Braves non-tendered Schlosser after the season and subsequently re-signed him to a Minor League contract, so he will be in the Rockies' camp as a non-roster invitee.
Briceno, 22, was signed out of Maracaibo, Venezuela, and spent last year at Class A Asheville. He hit .283 with 12 home runs, 23 doubles and a triple in 84 games. O'Dowd, 24, is the son of former Rockies general manager Dan O'Dowd, and he has played in 208 Minor League games with the Padres and Rockies organizations. He has batted .260 with seven home runs, 36 doubles and eight triples in 806 Minor League plate appearances. O'Dowd was selected by the Padres out of Dartmouth in the 23rd round of the 2012 Draft.