Hernandez, 33, went 6-13 with a 4.89 ERA in 32 starts (24 appearances) last season with the Rays. He made his last start Aug. 27 before Tampa Bay moved him to the bullpen.
Hernandez will join a rotation that includes Cole Hamels, Cliff Lee, Kyle Kendrick and Miguel Alfredo Gonzalez.
"It's more of a depth guy," Amaro said. "It's not somebody who is going to slide into the top of the rotation. But we need some depth. We're trying to get the best bang for our buck, and in this marketplace, it's tough because the prices have soared pretty significantly. We're just trying to add a little bit of depth."
Hamels and Lee are the aces, but there is uncertainty in the rest of the rotation. Kendrick had a 6.45 ERA in his final 14 starts last season before he stopped pitching because of a shoulder issue. Nobody knows what Philadelphia will get from Gonzalez, who has not pitched competitively in some time.
Then there is Hernandez. He made the All-Star team with the Indians in 2010, when he went 13-14 with a 3.77 ERA in 33 starts. He went 7-15 with a 5.25 ERA in 32 starts in 2011 before he missed most of the 2012 season because of the false identity arrest. Hernandez was arrested outside the United States consulate and could not return to the U.S. until he obtained a visa on July 21. He made three starts upon his return, but an ankle injury derailed the rest of his season.
The Phillies hope Hernandez can eat up innings, while Kendrick returns to form and Gonzalez pitches like Phils scouts said he can. Kendrick had a 3.50 ERA in 40 starts from April 29, 2012, through June 25, 2013. The Phillies liked Gonzalez so much that they originally agreed to sign him to a $48 million deal. But a problem with his physical dropped his price to just $12 million, although the Phils said Gonzalez is healthy.
"Who knows who's going to step up to be the No. 3?" Amaro said. "Miguel Alfredo Gonzalez could be that guy. We're just trying to look for depth in that area. If we have to go with threes, fours and fives to try to do that, that's what we'll do."
The Phillies made previous runs at Ryan Vogelsong and Scott Feldman. They had been interested in Bronson Arroyo, but it appears that pursuit is finished. They made no effort to sign Bartolo Colon, who signed a two-year, $20 million deal with the Mets.
If the Phils add any more starting pitching, it likely will be a guy who can shuttle between the bullpen and rotation, and free agents who likely will start the season at Triple-A Lehigh Valley.
"I don't know if we'll be adding another guy," Amaro said. "We've talked internally about some of our options. We'll likely have [Jonathan] Pettibone and Ethan Martin stretched out, and hopefully that will create enough depth for us. We're going to try to continue to look for some depth there. The likely signings we'll have there, if we can get this one done, will probably be free-agent invites, that sort of thing, to create some depth in Triple-A."
Amaro said he is "pretty comfortable" with the bullpen. It includes closer Jonathan Papelbon, who the Phillies have had no luck trading.
"We're still maybe looking to add one more piece, but again, most of those signings will probably end up being invites," Amaro said. "I think it behooves us to sit back, wait and see how things shake out. There's still a lot of players out there, and I don't know how many seats there are for them all. We're trying to be patient to see how things work out.
"Some of the big names, for us, are probably more names than they are talent. I would imagine with the prices that are out there, and what they're seeking, I don't think it matches up with the level of talent. That's my take on it. Someone's going to pay, I'm sure. Someone is going to get the players. We're just not targeting those, because we don't think it's the right bang for the buck."
The Phils believe Hernandez is.
Deals done: So far this offseason, the Phillies have signed right fielder Marlon Byrd, re-signed catcher Carlos Ruiz, acquired right-hander Brad Lincoln in a trade and agreed to a deal with Hernandez.
Rule 5 Draft activity: Philadelphia selected right-hander Kevin Munson from the Arizona Diamondbacks. Munson is a power pitcher, and he has a fastball in the 92-95 mph range with a good slider. He will compete for a bullpen job in Spring Training.
Goals accomplished: The Phillies believe Byrd will be a right-handed bat to protect Chase Utley and Ryan Howard. The club thinks Ruiz can stay healthy and productive after his worst season since 2008. Philadelphia expects Lincoln and Hernandez to provide depth to the bullpen and rotation, respectively.
Unfinished business: The Phils still need an extra outfielder who can play a true center field, while a pitcher who can shuttle between the bullpen and rotation would be welcome. Otherwise, barring a trade, the rest of the team's winter should be fairly quiet.
"We're still looking at things on the trade front, looking to add a little depth to our outfield, as we've talked about," Amaro said. "We'll continue to try to pursue that."
Team's bottom line: "We're built to win," Amaro said.