“I had no idea,” Robertson said. “I saw it and I was like, ‘Wow! Yes!’ ”

The White Sox now have two players developed by the Yankees who won a championship in navy pinstripes in 2009. (The Yankees themselves have just one — Brett Gardner.) Cabrera, Samardzija and Robertson tried on their black pinstripes at a news conference in Chicago on Tuesday. Duke and LaRoche signed earlier, in the first phase of a quick-strike winter for Hahn.

“You head into any off-season with certain areas of needs you were hoping to address, and we had a priority list for each area,” Hahn said during a conference call earlier in the day. “It was our intent and we’re pleased with how it’s been able to come through, but frankly I do think we probably have had a roll here that if you had told me six weeks ago we’d been able to convert on, I would have been a little bit surprised by.”

Hahn said that he had spent more than he expected, but that the fan response to the other moves inspired Jerry Reinsdorf, the team’s owner, to authorize Cabrera’s deal. The baseball buzz is not restricted to Wrigleyville.

“There’s a great deal of optimism around here and throughout the city, given the moves that are taking place on both sides of town,” Hahn said. “We’re all very eager for the season to get here, but there’s still a fair amount of time for each of us to continue to add and continue that momentum.”

The White Sox lack a proven second baseman, but they have two of MLB.com’s top five prospects at the position in Micah Johnson and Carlos Sanchez. The back of their rotation looks ordinary, but the left-hander Carlos Rodon, the first college player taken in last June’s draft, could make an impact soon.

The switch-hitting Cabrera, 30, will team with Adam Eaton at the top of the lineup, before Abreu, LaRoche and Avisail Garcia in the middle. Cabrera hit .293 over two seasons for Toronto — with 16 homers last year — after missing the end of 2012 while serving a drug suspension.