The contract terms weren't revealed, but ESPN reported Ellsbury will make $153 million and the club will have an option for 2021, while Kuroda will be paid $16 million.
Ellsbury, a 2010 all-star, led the American League in stolen bases last season with 52. He also compiled nine home runs, 31 doubles, 53 RBI and a .298 average for the World Series champion Red Sox.
In 715 career games with Boston since 2007, Ellsbury has 65 homers, 155 doubles, 241 stolen bases 314 RBI.
Kuroda, 38, was New York's most dependable starter last season, going 11-13 with a 3.31 ERA in 32 starts.
He cooled off late in the year, however, dropping his final six decisions.