The deal makes it more likely that Arizona will hang onto outfielder Justin Upton rather than trade him.
"I would say with all the areas we've addressed, I would say it's highly unlikely that we move Justin," D-backs general manager Kevin Towers said.
Arizona gave up right-handers Trevor Bauer, Matt Albers and Bryan Shaw in the deal, with all three going to Cleveland.
The Reds, who gave up Gregorius and sent outfielder Drew Stubbs to the Indians, received outfielder Shin-Soo Choo, infielder Jason Donald and cash considerations.
The move gives the D-backs another option at shortstop, which was one of their top offseason needs, while trading away a player they drafted just 1 1/2 years ago.
Gregorius was apparently at or near the top of the D-backs' list of shortstops they hoped to acquire this winter. Towers had numerous discussions with Reds GM Walt Jocketty about Gregorius, but the two teams were not a match.
Towers then talked to several other GMs about possibly getting Gregorius in a three-way trade.
Indians GM Chris Antonetti finally called Towers on Monday and said he thought he could get Gregorius. He then asked Towers if he would be willing to talk about trading Bauer.
Prospect acquired by Diamondbacks
- Didi Gregorius, SS: Gregorius, ranked No. 5 on the Reds' Top 20 at the time of the trade, continued to improve his stock as a prospect in 2012. The Curacao native, who signed with Cincinnati back in 2007, has always impressed with his athleticism and upside, and it was all on display as he played at three levels, including the big leagues during a September callup. There's no question he can stay at shortstop with a cannon for an arm and good range. He has above-average speed, which should help him on both sides of the ball in the future. He handles the bat well from the left side of the plate and understands the strike zone, though he can get overly aggressive at times. Named the No. 15 prospect in the Arizona Fall League this year by MLB.com, Gregorius will be just 23 for all of the 2013 season and should soon be ready to play shortstop every day at the Major League level. This could mean a move to second base for fellow D-backs shortstop prospect Chris Owings.
- Top 20 Prospects: Diamondbacks | Reds
- -- Jonathan Mayo
"I said the only way I would talk about Trevor Bauer is if I could get Gregorius," Towers said.
Gregorius, 22, made his big league debut last September with Cincinnati, going 6-for-20.
Born in the Netherlands and raised in Curacao, Gregorius created a stir with his flashy defensive work during big league camp last spring.
"At Spring Training, I learned a lot," he said in September. "They taught me a lot about how they play and how I have to play the game. I talked to them a lot and saw how everything is."
Gregorius began the 2012 season with Double-A Pensacola, where he had a slash line of .278 batting average/.344 on-base percentage/.373 slugging percentage before being promoted to Triple-A Louisville, where he hit .243/.288/.427.
Gregorius played for Peoria in the Arizona Fall League following the regular season, and he hit .284/.333/.392 in 74 plate appearances.
"He's certainly going to come into camp and compete with Willie Bloomquist, as well as Cliff Pennington, at shortstop," Towers said when asked if Gregorius was ready for the big leagues. "If he had to go back to Triple-A, I don't think it's such a bad thing. I think Triple-A at-bats would be good for him. Fortunately, we're in a situation where we've got depth at that area. Long term, having a guy like him and [Triple-A shortstop] Chris Owings, we've got two, I think industry-wide, two of the best young middle infielders in the game."
Gregorius' error total has decreased in each of the past three seasons, going from 32 in 2010 to 21 to 18.
A baseball talent evaluator said that Gregorius is a good athlete who could project to hit 10-15 homers eventually in the big leagues. The evaluator also said that Gregorius has outstanding range with a plus arm, and defensively, he could play in the big leagues right away.
"When I saw him, he reminded me of a young Derek Jeter," Towers said. "I was fortunate enough to see Jeter when he was in high school in Michigan. He's got that type of range, he's got speed, more of a line-drive-type hitter, and I think he's got the type of approach at the plate and separation to where I think there's going to be power there as well."
Sipp gives the D-backs another lefty in the bullpen to go along with Matt Reynolds, who was acquired last month from the Rockies.
Sipp, 29, had a 4.42 ERA in 63 games for Cleveland last season and held lefties to a .209 batting average while righties hit .250 against him. Over his four-year career, his splits are reversed, with righties hitting .209 against him and lefties hitting .215.
Anderson, 25, has played outfield and first base over a six-year Minor League career, during which he has hit .272/.369/.432.
Anderson, who has 56 career plate appearances in the big leagues, was originally drafted by the Red Sox and was traded to the Indians last July.
Bauer was the first of two top seven picks for the D-backs in the 2011 First-Year Player Draft. Selected out of UCLA with the No. 3 overall pick, Bauer signed quicker than most first-rounders and progressed up to Double-A Mobile in 2011.
Bauer pitched well during big league camp in 2012 and was 7-1 with a 1.68 ERA for Mobile before being promoted to Triple-A Reno, where he was 5-1 with a 2.85 ERA in 14 starts.
In four starts for Arizona in late June and early July, Bauer struggled with a 6.06 ERA.
During his time in the big leagues, Bauer clashed with veteran catcher Miguel Montero over game-planning, and at the end of the season, there was talk that the D-backs organization wanted Bauer to modify his intense pregame throwing program and alter his pitching style a bit.
Towers, though, said that played no role in the team's decision to trade him.
"Trevor is maybe a little bit more unique than most, but there have been a lot of guys in the big leagues that have been unique like him that have had great Major League careers," Towers said. "The only reason we did this is, it was a guy they asked about, a guy they had to have. We weren't shopping Trevor. There were other pitchers they asked about, but they demanded it had to be Bauer in this deal to get Gregorius. It had nothing to do with moving him because of routine or unwillingness to change. That didn't play into it at all."