The ambitious group immediately set a target of reaching the Championship within five years and appointed former England boss Eriksson.
County have also signed former Premier League players Sol Campbell, Lee Hughes, Kasper Schmeichel and Ade Akinbiyi this season.
Expectations were immediately raised following the takeover of a team who had finished in the bottom six of the Football League in four out of the previous five years - and it has not been all plain-sailing.
Disillusioned former England and Arsenal centre-back Campbell left the club after just one game - a 2-1 loss at Morecambe.
Then, manager Ian McParland, who played for County for eight years, lost his job in October despite the Magpies sitting fifth in the league.
He was replaced by Eriksson's friend and fellow Swede Hans Backe and County are now fourth in the table - two points off the automatic promotion spots.
Trembling, who arrived in the summer with the Munto Finance takeover, has already passed a Football League fit and proper person test.
He said: "Now we cherish ambitions to secure promotion this year and deliver sustainable progress into the Championship and beyond.
"This is clearly an important day for the club and one which will hopefully draw a line under several weeks of speculation.
"I must stress however that a great deal more still needs to be done if we are to fulfil our ultimate objective of Premier League football.
"We have restructured the ownership of the football club in order to secure new and prolonged investment. We anticipate this will be an ongoing process.
"The support and passion of our fans has constantly energised me. The last few weeks have been the hardest and most stressful of my working career but the support of the Notts County faithful has been the fillip that has driven me to complete what I anticipate being a significant stage on our road to progression.
"This is a totally unique project with the world's oldest professional League club and I, for one, am not prepared to walk away from that.
"We have seen our average home crowds double this season and it is absolutely imperative that our support base continues to grow.
I would like to thank my friend and confidant Sven-Goran Eriksson who has been steadfast throughout and with whom I will now embark upon the urgent process of securing new investment
"I would also like to thank the many sponsors, suppliers and our corporate supporters for their continued backing of our club.
"In particular I would like to thank my friend and confidant Sven-Goran Eriksson who has been steadfast throughout and with whom I will now embark upon the urgent process of securing new investment into the football club."
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