The 44-year-old former Celtic boss will be assisted by Garry Parker at Easter Road.
The Northern Irishman has been out of work since parting company with Bolton in March.
He succeeds Alan Stubbs, who left for Rotherham United last week after two seasons in charge, culminating in a Scottish Cup final triumph.
"As soon as Neil was identified as the outstanding candidate we were determined to bring him to Easter Road," said Hibs chief executive Leeann Dempster.
"He has managed at a very high level, taking Celtic to the last 16 of the Champions League, and we were attracted by his ability to get the most out of players and his driven, winning mentality."
Lennon served Celtic as a midfielder for six-and-a-half years, winning five Scottish titles and six domestic cups to add to the two League Cups he won with Leicester.
After a spell back in English football with Nottingham Forest and Wycombe Wanderers, Lennon rejoined Celtic as a coach in 2008, taking over as manager in 2010.
He enjoyed further success at Celtic Park with three successive top-flight titles and two Scottish Cup triumphs before leaving in the summer of 2014.
A move to Bolton followed later that year and, although Wanderers initially improved under Lennon, they were bottom of the Championship by the time he left, with the side eventually relegated.
Hibs have spent the last two seasons in Scotland's second tier and missed out on promotion to the Premiership after a play-off semi-final defeat by Falkirk, having also lost out at the same stage of the play-offs in 2015.
But after ending their 114-year wait to win the Scottish Cup, the Edinburgh club will enter the Europa League qualifying rounds, with their first match on 14 July.
Englishman Parker, 50, was a team-mate of Lennon's at Leicester and was part of his coaching team at both Celtic and Bolton.
Hibs have called a media conference for 14:00 BST on Thursday.
Neil Lennon has been confirmed as the new manager of Hibernian after signing a two-year deal.