The 19-year-old, who joined the Spurs Academy in July 2011, underwent surgery on March 11 to repair a fractured fifth metatarsal and is expected to remain in England to rehabilitate his foot before joining the American team.
"Grant is a young, technically-gifted player," said Fire head coach and director of soccer Frank Yallop.
"I watched him play in England, and throughout our preseason training camp, Grant consistently proved that he has what it takes to do well in MLS.
"We look forward to him joining our squad once he has recovered from his injury."
Grant made 17 appearances for the North London outfit's U18 side in 2012-13, including three games in the FA Youth Cup.