Less than three hours after the trade was announced, Suzuki made his Yankees debut against the Mariners in Seattle, and recorded his first hit for his new team.
The 38-year-old Suzuki has a .322 career batting average with 99 home runs, 633 runs batted in (RBI) and a .366 on-base percentage since entering the majors in 2001.
He won the American League Most Valuable Player (MVP) award and was named Rookie of the Year in 2001, joining Boston's Fred Lynn (1975) as the only players to win both honours in the same year.
Suzuki, the first Japan-born position player ever in the majors, is batting .261 with four home runs, 28 RBIs and 15 steals this season, in what was the last of a five-year, $90 million (£58m) contract.
In exchange for Suzuki, Seattle, sitting in last place in the AL West with a 42-55 record, received minor league right-handers D.J. Mitchell and Danny Farquhar.
Mitchell, 25, had a 3.86 ERA in four games out of the bullpen with New York this season, while Farquhar, also 25, was claimed off waivers by the Yankees last month from Oakland.
Seeking a first trip to the World Series before he retires and with the Mariners falling out of contention in the division, Suzuki had asked for a trade.
"On behalf of our ownership group and everyone in the Seattle Mariners organisation, I thank Ichiro for the great career he's had here in Seattle," Mariners chief executive Howard Lincoln said in a statement.
"Ichiro knows that the club is building for the future, and he felt that what was best for the team was to be traded to another club and give our younger players an opportunity to develop."
He will be expected to provide a boost to a Yankees team that just suffered a four-game sweep in Oakland but still enter the contest with a six-game lead in the American League East.
With the trade, Suzuki becomes the sixth Japanese player in Yankees franchise history, joining Hideki Irabu (1997-99), Hideki Matsui (2003-09), Kei Igawa (2007-08), Hiroki Kuroda (2012) and Ryota Igarashi (2012).