Igarashi, 30, was 47-29 with 54 saves and a 3.25 earned run average for the Yakult Swallows of the Japanese Central League from 1999-2009.
He recorded 630 strikeouts in 570 innings for an average of 9.95 strikeouts per nine innings.
"We've had an interest in Ryota for two years," Mets general manager Omar Minaya said in a statement. "He's got a power arm and an outstanding split-finger."
Igarashi, who had Tommy John surgery in 2007, was 3-2 with three saves and a 3.19 ERA last season. In 2008 he went 3-2 with a 2.47 ERA and three saves.
His career best in saves came in 2004 with 37.
"I have known the Mets scout...since I was in high school," Igarashi said through an interpreter, according to the Mets.
"When I received the Mets offer there was no doubt in my mind that this was the team I wanted to go to and start my career in the United States.
"I am looking forward to playing in New York and pitching in the same bullpen as (closer) Francisco Rodriguez."
(Writing by Larry Fine, Editing by Julian Linden)