Jackson, known as "Mr. October" for his World Series heroics, was with the Yanks through 1981. He hit 10 home runs in 27 World Series games with New York and Oakland.
"This is very big, it reminds me of the time we signed Reggie," Steinbrenner said at the team's minor league complex in Florida, the New York Post reported. "But it's an organizational deal, not a Steinbrenner deal."
Rodriguez, the American League's Most Valuable Player, has led the league in home runs the past three years.
He was acquired from the Texas Rangers for second baseman Alfonso Soriano and a player to be named.
The star infielder wanted out of Texas after three straight last-place finishes by the Rangers.
The Yankees are already selling a Rodriguez jersey on their Web site for $99.99.
Rodriguez is owed a guaranteed $189 million over the next seven years pushing the Yankees' payroll above $200 million.
Swim Week Miami Beach 2014 [PHOTOS]