Ellsbury made the switch between the bitter division rivals after winning the World Series with Boston this year, agreeing to the deal which also has a $21 million team option for the 2021 season, with a $5 million buyout.
The total package could be worth $169 million over eight years.
The 30-year-old has a .297 career batting average with 476 runs, 155 doubles, 65 home runs, 314 runs batted in (RBI) and 241 stolen bases in 715 games over seven seasons.
He led the majors last season with 52 stolen bases and in 16 playoff games hit .344 (22-for-64), leading all postseason players in hits and runs (14) en route to winning his second career World Series.
"I think it gives you tremendous defense in your outfield, where these guys are going to cover a lot of ground," Yankees manager Joe Girardi said on the club's official website.
"They (Ellsbury and current team member Brett Gardner) both can put a lot of pressure on a pitcher when they're on the basepaths, and their ability to go from first to third or first to home on a number of base hits.
"We think Jacoby's home run total will probably rise a little bit playing in this park compared to Fenway."
Kuroda, the 38-year-old Japanese starting pitcher, agreed to a $16 million one-year deal after going 11-13 with a 3.31 ERA in 32 starts with the Yankees in 2013.
He made nine scoreless starts, the most among all American League pitchers and second-most in the Majors behind only the LA Dodgers' Clayton Kershaw (10).