The Boston Red Sox stayed busy, reaching agreement with Jenks on a $12 million, two-year contract, a person familiar with the deal told The Associated Press on condition of anonymity because there was no official announcement.
The right-handed Jenks posted 27 saves for the White Sox last season, but lost the closer's role at the end of the year when he struggled with injuries.
The Red Sox agreed to a one-year contract with right-handed reliever Matt Albers, who made 62 appearances for Baltimore, and sent utilityman Eric Patterson to San Diego to complete the trade for first baseman Adrian Gonzalez.
Wood is going back to the Cubs on a one-year deal with a base guarantee of $1.5 million, a person familiar with the negotiations told the AP.
The 33-year-old Wood was the NL Rookie of the Year with the Cubs in 1998 and nearly helped pitch them into the 2003 World Series. Wood, whose career has been slowed by injuries, split last season with Cleveland and the Yankees. He's expected to be a late-inning reliever in Chicago.
The A's, who had trouble scoring this year, have added Willingham and David DeJesus to their outfield in the offseason. Willingham hit .268 with 16 homers and 56 RBIs for the Nationals.
"I think this team is ready to win," Willingham said. "And the organization, with the moves it has already made this offseason, proves it is ready to win also."
Ordonez and the Tigers agreed on a $10 million, one-year contract, a person familiar with the deal told the AP.
Detroit declined Ordonez's $15 million option in October, but wanted the six-time All-Star outfielder back if he recovered from a season-ending ankle injury in July.
Ordonez turns 37 next month. He hit .303 with 12 homers and 59 RBIs in 84 games last season.
Nishioka and the Twins reached a preliminary agreement on a three-year contract worth about $10 million, a person familiar with the negotiations told the AP. He hit .346 last season in Japan.
Nishioka can play shortstop or second base, and the Twins have a need for middle infielders after J.J. Hardy was traded and Orlando Hudson became a free agent.
Minnesota also traded backup catcher Jose Morales to Colorado for minor league left-hander Paul Bargas.
In other moves, the Yankees completed a contract with former All-Star catcher Russell Martin, Cleveland agreed to terms with infielder Adam Everett on a minor league deal and Toronto brought back designated hitter-first baseman Edwin Encarnacion.