The England Under-19 forward brings the curtain down on 12 years at Upton Park, with compensation due to be agreed between the two sides.
Hall rose through the Hammers ranks to make his first-team debut on New Year's Eve in 2011 and made a total of seven appearances for the club.
Having spent time on loan at Oxford and MK Dons in previous years, the 19-year-old enjoyed an impressive spell at Birmingham last season before completing the campaign on loan at Bolton.
He made just one brief npower Championship appearance for the Trotters but it was enough to convince boss Dougie Freedman to make a permanent move for his services.
The Hammers' official website read: "West Ham United would like to thank Rob for his hard work and wish him every success in his future career."