Fernandes, 21, has been a target all summer for the Hammers, who sit at the bottom of the Premier League table after two games.
West Ham saw two bids rejected earlier this month, but have now tabled a total package deal worth over £40million for the Portugal youth international.
The midfielder has indicated his desire to move on from Saints following the club's relegation from the Premier League and interest elsewhere.
The funds Saints received for Fernandes will allow them to sign three players in the next 48 hours, with deals in place for Finn Azaz and Caspar Jander.
Fernandes missed Southampton's Carabao Cup tie against Norwich City on Tuesday with Will Still insisting it was not a transfer-related decision.
The former Sporting prospect has played four times for Saints this season, and scored the winning goal in their first round tie against Northampton.
Fernandes will join Kyle Walker-Peters at West Ham after the two-time England international joined the London club on a free transfer this summer.