Soriano will be an eighth-inning setup man for longtime closer Mariano Rivera.
According to a baseball official, the idea is that if Rivera retires after his two-year deal expires, Soriano, 31, will be the heir apparent at closer.
In fact, Rivera in some sense chose his own successor, going to bat for Soriano with Yankees brass to convince the team to sign him, a source with knowledge of the negotiations told ESPNNewYork.com's Wallace Matthews.
Sources told ESPN The Magazine's Buster Olney on Friday that there was a split of opinion in the Yankees organization over signing Soriano with ownership prevailing over baseball operations.
Before signing Soriano, the Yankees had talked about a possible sign-and-trade that would have netted them Grant Balfour. If completed, the Yankees would have saved their No. 1 draft -- a stated priority of general manager Brian Cashman last week. The Yankees tabled the Balfour talks, instead, as they negotiated the Soriano deal.
Balfour ended up agreeing to a deal with the A's, sources told ESPN.com's Jayson Stark on Friday.
Soriano must still pass a physical to complete the contract.
Soriano has player options after the first and second years of the deal, according to the source. In the first year, Soriano will receive $10 million and get an additional $1.5 million if he opts out. In the second year, he'll receive $11 million and an additional $1.5 million if he opts out. He'll get $14 million in the third year of his contract.
An official said the player options were the Yankees' idea because they wanted Soriano to be comfortable. At least one official in the organization thinks they have the best bullpen in baseball.
Soriano's contract does not include a no-trade clause, a source told Olney.
SI.com first reported the deal.
For now, Soriano is likely to replace Kerry Wood as Rivera's top setup man. Wood, acquired by the Yankees from Cleveland at last year's trade deadline, became a free agent this offseason and went back to the Chicago Cubs, signing a $1.5 million, one-year contract.
Soriano, however, would give the Yankees extra insurance on days when they might want to rest Rivera. And with New York's rotation still somewhat uncertain -- Andy Pettitte isn't sure if he'll return for another season, Javier Vazquez signed with Florida -- Soriano would help add length and depth to a bullpen that might need to pitch extra innings for shaky starters.
Earlier this winter, New York signed left-handed specialist Pedro Feliciano to an $8 million, two-year deal.
Soriano was successful on 45 of 48 save chances last season in helping Tampa Bay edge out the wild-card Yankees for the AL East title. The 31-year-old righty was 3-2 with a 1.73 ERA in his only year with the Rays and was a member of the AL All-Star team.
The deal would mark the first major free-agent addition for the Yankees this offseason after they missed out on ace Cliff Lee.
Soriano becomes the latest prominent player to leave the cost-cutting Rays, who have won two of the past three AL East titles. Speedy outfielder Carl Crawford and first baseman Carlos Pena departed as free agents this offseason, in addition to relievers Joaquin Benoit, Dan Wheeler and Randy Choate. Starting pitcher Matt Garza and shortstop Jason Bartlett were traded.
AL East rival Boston has been especially busy this winter, signing Crawford and trading for All-Star first baseman Adrian Gonzalez.
Soriano made his major league debut with Seattle in 2002 and didn't start closing on a somewhat regular basis until 2009 with Atlanta. He had 27 saves with a 1-6 record and a 2.97 ERA that year with the Braves, then was traded to Tampa Bay after the season.
Information from ESPNNewYork.com's Andrew Marchand and Wallace Matthews, ESPN's Buster Olney and The Associated Press contributed to this report.