Breslow, 31, came to Arizona in a five-player trade with Oakland last December that sent All-Star Trevor Cahill to the desert and Jarrod Parker, the ninth overall pick in the 2007 amateur draft, to Oakland.
Breslow was 2-0 with a 2.70 ERA in 40 appearances for the Diamondbacks this season after signing a one-year deal.
"You never can have enough left-handers in the bullpen," Red Sox manager Bobby Valentine said.
General manager Ben Cherington said the Red Sox bullpen was at its best this season when it had three lefties. Breslow's acquisition plus the presence of Franklin Morales and Andrew Miller give the Red Sox three again now that lefty Rich Hill is on the disabled list.
Breslow also provides depth in case Valentine wants to return Morales to a rotation that has been inconsistent. Morales has spent most of the season as a reliever but is 2-1 with a 3.42 ERA in five starts. In 27 relief appearances, he is 0-1 with a 3.26 ERA.
Breslow is a native of Trumbull, Conn., played at Yale and pitched for the Red Sox in 2006, going 0-2 with a 3.75 ERA in 12 innings, all in relief. He wasn't available for Tuesday night's game against the Detroit Tigers, so the Red Sox recalled righty Clayton Mortensen from Triple-A Pawtucket.
Albers, 29, played for Houston and Baltimore before joining the Red Sox in 2011. He was 2-0 with a 2.39 ERA in 40 appearances for the Red Sox this season and has the second-most relief appearances of an inning or more since 2008 with 94.
He said he wasn't expecting to be traded and called the Red Sox "definitely the most talented team I've ever been on."
But he's excited about the move.
"It's a new opportunity, obviously, facing some different hitters" in the National League, he said. "That's going to be a little bit of an adjustment, but I think I'm ready for it.
"I think (the Diamondbacks) have a pretty solid back end of the bullpen so I'll probably be fitting into the same spot, filling the same role (as a middle reliever)."
Podsednik hit .387 with one homer and seven RBIs for Boston this season after being acquired for cash from the Phillies on May 11. The 36-year-old went on the disabled list with a strained left groin on May 11 and played for Triple-A Pawtucket after returning.
Josh Beckett started for the Red Sox on Tuesday night after his name had been prominently mentioned in trade speculation. He began the night with a 5-9 record and 4.57 ERA.
"We had conversations with a number of teams about a number of players," said Cherington, who declined to specify those players. "There was no intent to trade one guy or another."
The Red Sox also made a deal of minor-leaguers, sending first baseman-outfielder Lars Anderson to the Cleveland Indians for right-handed knuckleballer Steven Wright.
"The action on his knuckleball, we think, is major league quality," Cherington said. "We're hopeful we got a major league starter out of the deal."
Cherington also said righty reliever Scott Atchison will get a second opinion on what has been diagnosed as an injury to the ulnar collateral ligament in his pitching elbow. Atchison had a 1.76 ERA and 2-1 record in 37 relief appearances before going on the disabled list on July 15.