O’Neill agreed a one-year contract with the option of a further year’s extension.
He spent two spells in temporary charge of Celtic during a chaotic campaign that ended in spectacular fashion.
“It is once again a great privilege for me to continue as Celtic manager,” O’Neill said Thursday.
“Last season will live long in all our memories and to be part of that success has in a big way whetted the appetite to work again for more days like those and bring our supporters those moments.”
O’Neill, who had already enjoyed a successful stint at the Glasgow club from 2000-2005, first returned to Celtic Park in October after Brendan Rodgers’s exit.
Despite winning all eight of his domestic matches, O’Neill left when Wilfried Nancy was hired on a full-time basis.
However, Nancy was quickly axed following a miserable run and O’Neill returned in January.
O’Neill inspired a remarkable title-winning campaign as Celtic pipped Hearts on the final day of the season with a dramatic win against the Edinburgh club.
Hearts, chasing a first title since 1960, led the way for much of the season but Celtic benefitted from a hugely controversial penalty to beat Motherwell in their penultimate game.
O’Neill’s men came back from a goal down to beat Hearts in Glasgow in a last-day showdown, securing the club’s fifth successive title.
Seven days later, O’Neill secured his ninth trophy as Celtic manager when the Hoops beat Dunfermline 3-1 in the Scottish Cup final.
Former Celtic striker Robbie Keane had been linked with the job in recent weeks.
But pro-Palestinian Celtic fans opposed that potential move due to Keane’s spell in charge of Israeli club Maccabi Tel Aviv.
Urging Celtic to build on last season’s double, O’Neill said: “Celtic can never rest on past success so we are aiming to drive forward together as we aim to deliver again for the club and our fans.
“I thank our fans for their ongoing support, it means everything. I look forward to being back at Celtic Park, when we will come together and strive to bring our fans the success which that support deserves.”
Celtic’s principal shareholder Dermot Desmond vowed the club will back O’Neill’s vision in the transfer market.
The Celtic hierarchy has endured criticism from fans over their failure to spend big money on signings in the past.
“Time and time again Martin has shown his qualities,” Desmond said.
“We know he is a winner, we know what the club means to him and he continues to be the outstanding candidate.
“He knows the demands at Celtic and I know how determined he is again to bring success to the club and our supporters.
“The club will support Martin fully again across the close season to make sure we are well prepared to achieve domestic success and compete on the European stage.”
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