The New Zealander takes over from Declan Kidney whose five-year tenure that began with a first Six Nations Grand Slam in 61 years ended this month with his side narrowly avoiding a first wooden spoon since a whitewash in 1998.
Schmidt, who guided Leinster to their second and third European titles in four years during his first two seasons in charge, will take over from July on a three-year contract, the Irish Rugby Football Union said in a statement.
"It's a bit like when I came to Leinster, I didn't ever really want to be a head coach but I've really enjoyed the experience," Schmidt, who served on the coaching staff at Clermont Auvergne in France and New Zealand's Auckland Blues before coming to Ireland, told a news conference.
"I'm really motivated by challenge, I think this is a super challenge, albeit, an intimidating one and I guess if you're going to really find out what you think you can bring to a group, what better way that try to take on one of the big jobs in world rugby."
Schmidt had intended to return home to New Zealand after one more season with Leinster but has said recently that he found the change of pace of international rugby attractive as he could spend more time with his youngest son who suffers from epilepsy.
The favourite for a post that also attracted the interest of Queensland Reds' coach Ewen McKenzie, Schmidt is admired by many for playing the kind of attacking rugby Kidney was criticised for not bringing to the national team.
The softly-spoken Kiwi, who briefly played and coached in the Irish lower leagues during the 1990s, returned with the aim of making Leinster the best passing team in Europe and succeeded in bringing an extra verve to the 2009 Heineken Cup champions.
Schmidt's Leinster were untouchable in a 17-match unbeaten European run that spanned two years and was ended by his former club, Heineken Cup finalists Clermont, last December.
In his first European triumph, the Irish province turned around a 22-6 halftime deficit to stun Northampton in the 2011 final and last season they swept aside Ulster 42-14, the biggest margin of victory in a Heineken Cup decider.
Schmidt has taken Leinster to the final of the Amlin Cup this season and had been Kidney's expected replacement despite having run-ins with the Irish Union over overseas player limits for the regional sides.
Ireland's Grand-Slam winning captain Brian O'Driscoll said last week that he learned more in three years under the former school headmaster than he did from any other coach in the previous decade.
O'Driscoll will decide in July whether or not to retire and Schmidt joked that he planted the supporters in the Leinster crowd who started the "one more year" chant on Saturday encouraging the centre to play on beyond this season.
"He'll make his own decision but at the same time it doesn't stop you trying to push him towards one," Schmidt said.
"I'd like to see him continue, I'd love to see him named tomorrow (in the British and Irish Lions squad), I think that would be part of a continuation of a stellar career, hopefully not the end of one."
The IRFU said Kidney's assistant Les Kiss would take charge of the team, as planned, for their June tour of North America to allow Schmidt to finish the season with Leinster and select his backroom team.
Schmidt's first game in charge will be at home to Samoa in November before welcoming Australia and his native New Zealand to Dublin later that month.
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