The England goalkeeper will join the Hammers on a season-long loan, with the move expected to be announced officially on Monday evening.
With his current contract with the Citizens running until 2019, both clubs will share the keeper's £120,000-per-week salary, while West Ham also have the option to sign him on a permanent basis at the end of the season.
Surplus to Guardiola's requirements, the move will prove an opportunity for Hart to protect his place in the England squad ahead of next year's World Cup.