A statement on the club's website said Kinnear would be in charge of all football-related matters and would report directly to the club's board, with manager Alan Pardew reporting to Kinnear.
"The board are pleased to welcome Joe back to the club," managing Director Derek Llambias said.
"Joe has many years of experience working within the game, and this experience will be of great benefit to the club in achieving our objectives over the coming seasons."
The announcement comes a day after Kinnear gave a bizarre radio interview in which he rounded on his critics.
He also made a series of gaffes in which he pronounced the names of players and club officials incorrectly and claimed credit for a signing in his former spell as manager when the player was actually recruited by another.
Kinnear said he had put pen to paper on Sunday, yet there remained no mention of the deal on the club website until Tuesday.
Kinnear managed the club for four months during the 2008/09 season, his tenure ended by a heart attack.
Some fans have criticised the decision to bring him back after his first spell, which was marked by an expletive-ridden news conference rant when he swore 52 times at reporters.
Kinnear, who has had spells as manager at Nottingham Forest, Luton Town and Wimbledon, had little time for his critics.
"I don't know what angle they've got," he said on talkSPORT. "If they want to sit down and argue with me, some of them are talking out their backsides, a load of tosh and I'm not accepting it.
"It's as simple as that. I've certainly got more intelligence than them, that's for sure."
Kinnear was first appointed at St James' Park after Kevin Keegan left in September 2008 but stepped aside in early 2009.
In his initial spell in charge he upset former Newcastle player Charles N'Zogbia by referring to him on television as Charles 'Insomnia'.
On Monday, he called current player Hatem Ben Arfa 'Ben Afri' and Yohann Cabaye 'Kebab'.
He also said he brought Tim Krul to the club, when the goalkeeper was in fact recruited two years before Kinnear arrived.
Kinnear's appointment has also shed doubt on Pardew's position within the club and what role the manager will have in shaping the squad ahead of next season.
Kinnear said he had spoken to Pardew, who was rewarded with an eight-year contract last season, on the telephone and would meet him for lunch on Tuesday when they would put together their plans for the new campaign.
All decisions on player transfers, he said, would be joint ones.
"No one's got an ego," he said. "I haven't got an ego. We'll discuss areas what's desperate - in my opinion we need a striker and I see that desperate - as my opinion - when I speak with Pards tomorrow he may see some other position that he wants or get a better player for that area."
Newcastle became embroiled in a relegation battle last season after finishing the previous campaign in fifth, heaping pressure
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