Wood, a hard-throwing, 33-year-old righty, gives the Yankees another setup option alongside Joba Chamberlain for closer Mariano Rivera.
The Yankees sent Cleveland a player to be named or $500,000, and the Indians gave New York $2,172,131. New York will pay $1.5 million of the $3,672,131 remaining on Wood's $10.5 million salary this year. His contract includes an $11 million team option for 2011.
New York also finalized its deal to obtain designated hitter Lance Berkman from Houston along with $4 million for reliever Mark Melancon and minor league infielder Jimmy Paredes.
A day earlier, the Yankees obtained outfielder Austin Kearns from the Indians for a player to be named.
Wood was activated from the disabled list by the Indians on Saturday. He had been sidelined by a blister on his right index finger.
It was his second time on the DL this year. He didn't pitch until May 8 because of a strained muscle in his upper back.
Wood was 1-4 with a a 6.30 ERA and eight saves in 23 relief appearances for Cleveland. New York opened a roster spot by designating right-hander Chan Ho Park for assignment.
Cleveland has until Oct. 15 to decide whether to select a player from a designated list or to take the cash.
AP freelance writer Mark Didtler in Tampa, Fla., contributed to this report.