City of London Police made the announcement on Friday and in a statement said no arrests had been made.
Former England manager Sam Allardyce, the most high-profile figure involved, said he was not the subject of the inquiry. But it remained unclear which of the allegations - two of which concern Barnsley and Leeds United owner Massimo Cellino and Barnsley - is under investigation.
In September, the newspaper published a series of stories about alleged corruption in football that included a claim that eight current or former Premier League managers have accepted bribes in transfer deals.
The Telegraph’s investigation also resulted in Barnsley’s assistant manager Tommy Wright being sacked by the Championship club after he was filmed accepting a £5,000 payment to apparently help the fake investment firm place players at the club.
Other individuals named by the newspaper were Southampton assistant manager Eric Black, Leeds chairman Massimo Cellino and former QPR manager Jimmy Floyd Hasselbaink.
Black was filmed allegedly explaining how to bribe lower-league clubs in transfer deals, Hasselbaink discussing a deal to become an ambassador for the phoney investors and Cellino suggesting they take a stake in the Yorkshire club to benefit from player transfers.
All three have denied any wrongdoing and it is unclear what if any rules they may have broken. Hasselbaink has since lost his job at QPR but that is related to the club’s results under his guidance.
But the most high profile story centred on former England manager Sam Allardyce allegedly offering advice to a group of fictitious foreign investors on how to circumvent rules on the third-party ownership of players, a practice that is now banned worldwide.
Allardyce has strongly denied any wrongdoing but the controversy surrounding the newspaper sting, and some other indiscreet remarks that were caught by the undercover reporters on a hidden camera, cost him his job with the national team after just 67 days.
But when asked if Allardyce is the subject of the investigation, a City of London Police spokesman confirmed that the 62-year-old Englishman has received a letter that states he is not being investigated.
Allardyce said in a statement: “I welcome today’s confirmation from City of London Police that I will not be the subject of a police investigation. I was always confident that this would be the case as there was no evidence against me. I now ask that the Football Association deals with this matter as quickly as possible.
“I would like to thank my friends and family who have stood by me during this difficult period. The position of England head coach is the pinnacle of any English manager’s career and it was my dream job. While I am sad that my tenure came to an end early, I am nonetheless proud to have been chosen to manage the England football team and hope that today’s confirmation from the police will give me the opportunity to move on.”
The chairman of Belgian second-tier club Oud-Heverlee Leuven, Jimmy Houtput, was another named by the newspaper and he resigned when he was caught on camera appearing to offer his club as a “conduit” for getting around the third-party ownership restriction.
The confirmation that the City of London Police has completed its review of the Telegraph’s evidence will be welcomed by the Football Association, English Football League and Premier League who have all been waiting to receive it so they can proceed with their own inquiries.