Ohlendorf has passed his physical and the Reds didn't have to make room for him on the 40-man roster. They are currently at 39 active players.
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Price and the club's baseball hierarchy are still trying to determine a five-man rotation to open the season.
The third-year manager has yet to name a starter for the season opener against the Phillies in Cincinnati on April 4, although it likely will be right-hander Anthony DeSclafani.
Ohlendorf was in camp with the Royals this spring and opted out of his Minor League contract. He was released on Wednesday. He made eight relief appearances, allowing six earned runs on nine hits while walking three and striking out 10 in his nine innings pitched.
Price said he didn't think Ohlendorf has pitched enough innings to start at this point and that's the primary reason he'll go to 'pen.
"I don't believe we have the time," said Price, who's club breaks camp after a game here against the Indians on Thursday. "We've looked at this season as an evolution of our young position players, but even more so our young pitchers. That's going to come sequentially.
"Our challenge is to get other pitchers into that bullpen that are reliable to get to [closer] J.J. [Hoover]. And I think that's why Ross is attractive, at least to me right now, as a relief pitcher even though he has value as both."
Ohlendorf has pitched in the Majors for five teams, most recently as a reliever for the Rangers last season when he was 3-1 with a 3.72 ERA with a save and 19 strikeouts in 19 1/3 innings (21 appearances).
He last started exclusively for the Pirates from 2009-2011 and made seven starts for the Nationals in 2013. He missed the entire 2014 season because of a back strain and was released by Washington after that season.
Considering injuries to projected Reds starters -- including Homer Bailey rehabbing from Tommy John surgery and not expected back until May 1 -- the Reds may continue to scan the market and waiver wire for available starters.
Price said he was "pleasantly surprised" by the Ohlendorf signing.
"In our situation we always want to look to improve our club, but we have to be fiscally responsible," Price said. "There are limitations on what we are capable of doing."
Rotation hopefuls -- Michael Lorenzen (sore elbow) and Jon Moscot (intercostal strain) -- are also both seemingly out of the picture for the first weeks of the season, at this point.
Moscot, who hasn't pitched in a live game since March 8, is expected to start here in a Monday night game against Milwaukee. Price said he hopes to give Moscot two starts before the start of the regular season, although Moscot opening in the rotation right now seems unrealistic.
The Reds play a pair of exhibition games against the Pirates in Pittsburgh on April 2-3.
"For [Moscot] to pitch where I anticipated him starting in the rotation, a lot of good things would have to happen," Price said.