He'll make his anticipated debut when he starts the opener of a three-game series against the host Colorado Rockies on Monday night.
Beckett had his run-ins with Red Sox fans and management during his tenure, from reportedly drinking beer and eating fried chicken in the clubhouse during Boston's late-season collapse in 2011, to being publicly chastised in May for playing a round of golf one day after missing a start due to a reported injury.
"It was time for me to move on and start a new chapter," Beckett said.
Part of the backlash Beckett (5-11, 5.23 ERA with Boston) has received is due to his overall poor performance on the mound. He hasn't won since beating Tampa Bay on July 15, going 0-4 with a 7.59 ERA over his last six starts. He gave up four runs in six innings of a 4-1 loss to the Yankees in his last outing Aug. 19.
Despite his current numbers, manager Don Mattingly is excited to have the veteran.
"Josh has thrown a lot of innings," Mattingly told the team's official website. "When you look at Josh, he has always been able to throw the ball where he wants. When you can locate, you can get people out."
The 32-year-old Beckett said he has plenty of solid innings remaining.
"I don't think anyone has the same stuff at 21 and 32," Beckett said. "You just learn how to make different adjustments. I think you learn how to do that when you are younger as well. It's an ongoing thing."
The right-hander is 5-1 with a 3.48 ERA lifetime versus Colorado, last facing the Rockies in Game 1 of the 2007 World Series and guiding the Red Sox to victory.
The Dodgers hope Beckett can get off to as good of a start as Gonzalez. The first baseman homered on the second pitch he saw in Saturday's 8-2 win over Miami, then went 2 for 4 with an RBI in Sunday's 6-2 defeat in the series finale.
Los Angeles (69-59) trails St. Louis by 1 1/2 games for the NL's second wild-card spot, and it will look to bounce back against a Rockies team that has won six of eight despite Sunday's 5-0 loss to the Chicago Cubs.
Colorado (51-75) mustered only four hits - its fewest since July 24 - and was shut out for the first time since July 27.
''Let's face it, we got four hits today, three of them came with two outs and nobody on," manager Jim Tracy said. "You're not going to be able to do a whole lot when you get three of your four hits with two outs and nobody on.''
Jeff Francis will oppose Beckett looking to build on Wednesday's performance when he allowed one run in five innings of Colorado's 5-2 win over the Mets.
Francis (4-4, 5.79), who lost to Beckett in their World Series matchup nearly five years ago, gave up three runs in four innings of the Rockies' 6-4 loss to the Dodgers on Aug. 8 as Los Angeles salvaged the series finale.
The left-hander is 2-3 with a 6.99 ERA in eight home starts.