The Blades had wanted £45m in lost revenue following relegation from the Premier League after Tevez had kept West Ham up with a series of match-winning displays.
They claimed the Argentine had no right to be playing because his deal with the Londoners was in breach of Premier League third-party rules.
That view was backed last year by an independent FA tribunal chaired by Lord Griffiths.
But West Ham argued the real cost of relegation, with savings from wages and recruitment taken into account, was no more than £5m.
The Griffiths panel was due to meet on Monday to discuss the level of damages due to Sheffield.
However, Hammers chief executive Scott Duxbury and Blades chairman Kevin McCabe thrashed out a deal and the money will be paid in three instalments.