The League Two club said Eriksson, 61, would be joined by his long-term assistant Tord Grip, who will assume the role of general adviser.
Eriksson said: "I am particularly attracted to this role and the unique opportunity to help build a club over the longer term."
The Magpies were taken over by a Middle-Eastern consortium a week ago.
Eriksson will start his role with immediate effect, will also be a shareholder and his remuneration will be determined by the success of the team.
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The Swede will be responsible for transfer negotiations and scouting, health, fitness and development of players, training facilities, the youth academy and establishing community and overseas links.
The future of manager Ian McParland is unclear under the new regime but a news conference will be held by the club at 1200 BST on Wednesday.
Eriksson started his managerial career in lower-league football with Degerfors in his homeland and won promotion at the first time of asking.
"I can think of no better challenge than to attempt to do that again but this time with the world's oldest football club, where we can add to a proud tradition and hopefully bring some richly deserved success," he stated.
Eriksson, who spent five years in charge of the England team and also had a spell as manager of Manchester City, was sacked as coach of Mexico in April.
Following that dismissal he had been linked with a return to the Premier League with Portsmouth.
Signing Eriksson is a massive coup for the Magpies because of his record of success across European football.
ERIKSSON'S TEAMS
Degerfors 1977-78
IFK Gothenburg 1979-82
Benfica 1982-84
Roma 1984-87
Fiorentina 1987-89
Benfica 1989-92
Sampdoria 1992-97
Lazio 1997-2001
England 2001-06
Manchester City 2007-08
Mexico 2008-09
He made a name for himself in his homeland with IFK Gothenburg before moving to Benfica, where he won two Portuguese league titles, a Portuguese cup and the team finished runners-up in the Uefa Cup.
A spell in Italy followed before he returned to Benfica, leading them to the final of the European Cup in 1990, which resulted in a 1-0 defeat at the hands of AC Milan.
It was at Italian side Lazio where Eriksson arguably achieved his greatest success, winning every major trophy in Italy - including the Serie A title in 2000 for only the second time in the Rome club's history - and the European Cup Winners' Cup.
He became the first foreign manager to take charge of the English national side when he was appointed as Kevin Keegan's successor in 2001.
He spent five years at the helm, leading England to the quarter-finals of the 2002 and 2006 World Cups, as well as a place in the last eight at the 2004 European Championship.
Eriksson announced his decision to step down as England manager before the 2006 World Cup in Germany - two years before his contract was set to expire.
A year out of the game followed before he joined Manchester City in July 2007 but he spent only one season at the helm before being replaced by Mark Hughes.
In June 2008, Eriksson replaced Hugo Sanchez in the Mexico job, the legendary striker having been sacked three months earlier, but he lasted less than a year.
The consortium Munto Finance is believed to have wiped out County's debts of about £1m when taking over from a supporters' trust earlier this month and has pledged to finance a sustained bid for Championship football over the next five years
Notts County chairman Peter Trembling said: "Sven and his team join us with an unrivalled football pedigree.
"Their knowledge of the game and contacts throughout the football world will significantly enhance Notts County's prospects.
"Sven shares our vision and to attract someone of his calibre is testament to the ambition that we all share for Notts County. This is a great day for everyone associated with the club."