Bichette gives the Red Sox a run producer and a candidate for designated hitter. Boston has tried several players as the DH all season without satisfaction.
The 36-year-old outfielder approved the trade Thursday afternoon. Because he was traded before midnight, he'll be eligible for Boston's postseason roster if the Red Sox make it that far.
"His wife is from the Boston area, the Red Sox are in (contention) for the wild card, he has a chance to play on grass instead of turf and he'll be hitting between (Carl) Everett and (Nomar) Garciaparra," Reds general manager Jim Bowden said.
Bichette is hitting .295 with 16 homers and 76 RBIs and has batted cleanup for the Reds most of the season.
Boston began the day 1 1/2 games behind Cleveland in the wild card race and five games behind New York in the AL East.
Bichette had a .366 career average (26-for-71) with three home runs at Fenway Park when he played in the AL with Milwaukee and the Angels from 1988-92.
"The Red Sox are pleased to acquire Dante Bichette, a proven veteran RBI man with excellent offensive career numbers," Red Sox general manager Dan Duquette said. "We're looking forward to having him on the ballclub to contribute down the stretch now and also to help us next season."
The Reds got right-hander Chris Reitsma and left-hander John Curtice, neither of whom has made it above Double-A.
The trade ended a brief and unusual stay in Cincinnati for Bichette, who went to the Reds in an Oct. 30 deal with the Colorado Rockies.
Bichette approved that trade because it moved him closer to his home of Orlando, Fla. The Reds needed him at the time because Greg Vaughn, their cleanup hitter from 1999, had become a free agent.
Bichette became expendable when the Reds traded for Ken Griffey Jr. on Feb. 10 and gave him a nine-year, $116.5 million contract. Despite having the two run producers in the middle of their lineup, the Reds have struggled to stay above .500 all season.
They considered getting rid of Bichette after they extended shortstop Barry Larkin's contract in July, putting nex year's budget in a squeeze.
With many of their young players eligible for arbitration, the Reds were looking to unload some of their payroll.
"It certainly gives us the ability to retain our young players that are eligible," Bowden said. "Instead of having to worry about moving payroll at the end of the season, we're in pretty good shape going into next season."
Cincinnati, which had closed the gap on St. Louis in NL Central, has fallen off lately. The Reds went into Thursday night's game at Atlanta trailing the Cardinals by 8 1/2 games.
Reitsma, 22, was 7-2 with a 2.58 ERA in 14 starts for Double-A Trenton this season.
Curtice, 20, was 4-10 with a 6.49 ERA in 23 starts and two relief appearances for Class A Sarasota.
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