Tevez's agent Kia Joorabchian has paid West Ham a £2m settlement agreement, meaning the 23-year-old has been formally released from his contract.
United have put forward their proposed two-year loan deal for the Argentina striker to the Premier League.
The league's lawyers are now looking through the details of the signing before rubber-stamping the deal.
Tevez's fellow Argentina international Javier Mascherano was given the go-ahead for a similar signing for Liverpool last season, meaning there should be time for United to receive clearance before they kick off the new season this weekend.
The champions kick off their campaign against Reading at Old Trafford on Sunday.
Premier League chief executive Richard Scudamore said on Tuesday that the Tevez saga had been "unbelievable".
"What made this an unbelievable story was an unbelievable series of events," he told BBC Radio Five Live.
"West Ham were all-but relegated at Christmas and then Tevez scored a few goals right at the end of the season and they were able to escape.
"It's unscripted drama and one of the things that makes football so interesting but it other ways it looks like a road crash in how some of the events appear."
Last week's agreement between West Ham and Joorabchian ended the threat of High Court action.
The settlement was approved by the Premier League but it is still to sanction Tevez's move to United.
Tevez is understood to have passed a medical and even trained with United last Friday.
The Argentine was expected to make his debut for the club in a friendly on 8 August.
"We have a couple of games on Wednesday and Carlos will be involved in one of those," said Old Trafford boss Ferguson last week.
"He trained with us on Friday morning and he was very enthusiastic."
All sides were keen for the matter to be settled ahead of a proposed court date on 22 August and the closure of the transfer window at the end of the month.
Tevez's switch had stalled over who will be paid the transfer fee.
The Premier League and West Ham said the Hammers should receive the fee but companies MSI and Just Sports Inc, which belong to Joorabchian, said they owned the striker's economic rights.
Tevez arrived with Mascherano at West Ham last August, and his outstanding form towards the end of last season kept Alan Curbishley's side in the Premiership.
But there was always a shadow hanging over the deal after West Ham were fined £5.5m over the transfers of Tevez and Mascherano.
The club was found guilty of acting improperly and withholding vital documentation over the duo's ownership, but crucially avoided a points deduction.
(bbc news)
