The agreement, which still needs to be formally ratified by the Premier League and Football Association, will see the Hammers paid between £1million and £3million in compensation.
The deal will also mean the settlement of the £30million lawsuit brought against West Ham by Tevez's agent Kia Joorabchian.
Talks on Thursday ended with an agreement between both sides and on Friday the league and the FA should sign off the deal - Premier League lawyers have been kept up-to-date with the progress of discussions.
Joorabchian should then be able to try to sew up an agreement with United to allow the striker to join up before the start of the season.
In the unlikely event of either side having a last-minute change of heart, then the only other avenue would be a lengthy High Court battle and there has been an acknowledgement that that would be in no party's interests.
United have already indicated a desire to take Tevez on the same sort of loan package that saw Javier Mascherano move to Liverpool last season.
That deal took some weeks before it was signed off by the Premier League but with that transfer having already been picked over by the lawyers, a similar deal for Tevez should go through much quicker.
The agreement with West Ham brings an end to a long-running and painful saga for the club that began when former chairman Terry Brown signed Tevez and Mascherano under banned third-party agreements last summer.
The club were fined £5.5million as a result by a disciplinary commission in April and that led to an unsuccessful legal challenge by Sheffield United, who claimed they should have been docked points.