The Red Sox took two steps toward shoring up their bullpen Thursday, while also completing the trade for first baseman Adrian Gonzalez.

According to a major league source, the Sox have re-signed lefty Andrew Miller, whom they originally acquired from the Marlins in exchange for Dustin Richardson. Miller was non-tendered by the Red Sox in Nov., allowing the 25-year-old to become a free agent. He is expected to compete for a spot in the Red Sox’ bullpen.

The Red Sox also made the signing of reliever Matt Albers official, announcing they have inked the 27-year-old to a one-year deal. Alberts, a righty, went 5-3 with a 4.52 ERA in a career-high 62 appearances with the Orioles in 2010. Albers tossed more than one inning on 25 occasions  in ’10, tops among American League relievers.

Another move made by the Sox was trading utilityman Eric Patterson to the Padres to complete the Dec. 6 deal for Gonzalez. Patterson had been acquired by the Red Sox on June 26 of last season from the A’s, going on to hit .226 with two homers in 45 games. Between Oakland and Boston, Patterson established career highs in games played (90), at-bats (187), runs (26), hits (40), doubles (8), triples (5), home runs (6), RBI (16), and stolen bases (11) over the course of the ’10 season.

The team also re-signed Rich Hill, who pitched six innings for the team last season.

Additionally,they announced the signing of lefty reliever Randy Williams, who pitched 27 innings with a 5.40 ERA for the and White Sox last season, and right-handers Clevelan Santeliz and Ryan Harvey.

Harvey was the sixth overall pick by the Cubs in the 2003 draft. The team drafted him as an outfielder, but he never made it past Double-A.

For more Red Sox news, see the team page at weei.com/redsox.