The former Bolton, Everton and Celtic defender moves to the newly-relegated club from Everton, where he had been under-21 coach for six years.
The 42-year-old takes over from Terry Butcher, who was sacked following the club's demotion to the Scottish Championship.
Stubbs said on the Hibs website: "To be given this opportunity with Hibernian is a great privilege and a real honour - it is a massive club with huge potential."
Stubbs added: "I'm excited about the future here at Hibernian and what we can all achieve together at the club - this is the start of the journey.
"The Scottish Championship will be a tough division, but I'm confident that if we approach the challenge with enthusiasm, optimism and belief then we can achieve success.
"I've been at Everton for almost six years and now I believe I'm ready to take on the role of head coach here at Hibernian.
"I would like to thank Everton for giving me the chance to take up this position with Hibernian and now I just can't wait to get started; helping the club to earn promotion."
No details of the length of his contract were given, with the club simply stating he would take charge of the team for the "forthcoming 2014-15 Scottish Championship season".
Stubbs made his name as a defender before also enjoying successful spells at Celtic, where he won two league titles, and Everton.
Hibs chief executive Leeann Dempster said: "He is a driven, intelligent and strong-minded character, who has a very clear vision about what he wants to achieve in football - producing positive results, playing attractive football and developing young players.
"All those attributes fitted the criteria we required and we're confident Alan is the right man to unite the club and bring success to Hibernian.
"Alan will be our head coach and that is part of the new structure in place at the football club; a continental-style model designed for continued long-term success."
Stubbs helped develop the likes of England internationals Ross Barkley and John Stones during his time working with the youngsters at Goodison Park.
Everton boss Roberto Martinez said on the Toffees website: "We wish Alan the very best of luck. The reality is when you work well and do things well, people will take notice.
"It reflects the excellent work done last season at the club and means it has been seen from the outside as well.
"We're proud when those individuals that are Everton through and through get noticed and are given rewards and opportunities."
Hibs were relegated from the top flight after losing a play-off to Hamilton on penalties and will face Rangers and city rivals Hearts in the Championship next season.