The deal portrayed by both general managers as involving "classic change-of-scenery guys" featured right-handers struggling through similar seasons.
Both Grilli and Frieri have 11 saves. The 28-year-old Frieri, who is nine years younger than Grilli, has a 6.39 ERA while Grilli is 4.87.
Although their contracts are also similar, Frieri will be under club control for two more seasons, having been eligible for salary arbitration for the first time last offseason.
"If we can get him back on the right track, that is one of the potential upsides," Pittsburgh GM Neal Huntington said.
A National League All-Star last season as a first-time closer at 36, Grilli had blown four of his 15 save opportunities -- doubling his total for all of 2013 -- when Pirates manager Clint Hurdle decided to replaced him with Mark Melancon last Friday.
Since then, Grilli had made two appearances, both in mop-up roles with the Bucs trailing.
"Jason has responded well to a series of challenges in his life," said Huntington, shortly after delivering the trade news to the pitcher about a half-hour prior to the first pitch of the Bucs' game against the Mets. "He had a good run here. He loves the city and the team, but he is ready for a new challenge."
"In our case, we acquire a guy who over the last two years has been outstanding in Pittsburgh, who was an All-Star in 2013, and as dominant as any closer in the league at the halfway point last year who has been a little topsy-turvy at the start of this year, " said Angels GM Jerry Dipoto.
In many ways, Grilli was the face of the franchise revival that saw the '13 Pirates make their first postseason appearance in 21 years. As a free agent following the 2012 season in which the Pirates contended until a last-month swoon, Grilli re-signed with the team with the expressed intent of helping finish the job.
And the picture of him celebrating with catcher Russell Martin in Wrigley Field after the out that clinched the Pirates' first playoff appearance since 1992 will be forever etched in fans' memories.
Grilli spent nearly a month on the DL with a strained left oblique, and he did not appear to have the same zest following his May 23 return.
"The oblique strain threw him off track, and he got away from being as aggressive as he was before the injury," Huntington observed, "when he approached things with a nothing-to-lose edge. He wasn't quite as sharp."
Frieri notched 37 saves in 41 chances last season for the Angels, and during his career has converted 71 of 81 opportunities. The native of Colombia is not signed beyond this season, his 2014 contract at $3.8 million.
"Ernesto is a guy we've pursued for a couple of years and haven't been able to get him," Huntington said. "He's going through a rough stretch now, but there's a lot of things there that we like. He has quality stuff, a good strikeout rate -- he isn't the ground-ball guy we typically look to acquire, but induces soft contact.
"We feel like we've had some guys like this in the past who, with a change of leagues and scenery, can come in here and do a nice job."
"We're encouraged to get the opportunity to work with Jason Grilli, and see if we can't get him back to where he needs to be," Dipoto said. "I would say the same of the Pirates with Ernie. Ernie will turn it around."
Grilli signed a two-year, $6.75 million deal as a free agent prior to the 2013 season. After posting a 2.91 ERA as a premier setup man in 2012, the Bucs had re-signed him with the specific intent of having him succeed Joel Hanrahan as the team's closer.