Holt is a free agent after rejecting a new contract last season but Hearts are due compensation as the midfielder came through the youth ranks at Tynecastle.
The 22-year-old, who spent the second half of last term on loan at Sheffield United, has been training with Rangers for several weeks and is now able to finalise a deal.
A statement from the Championship winners on Tuesday read: “Heart of Midlothian Football Club can tonight confirm that a development fee has been agreed with Rangers for Jason Holt.
“The Scotland U21 cap will now hold signing talks with the Ibrox side.
“Jason made 71 competitive appearances in a maroon shirt and scored seven goals, after making his first-team debut in 2011.
“The club thanks Jason for his time at Hearts and wishes him well in the future.”
Holt started the Ibrox side’s 1-0 friendly defeat against Burnley on Tuesday night and could make his competitive debut against Hibernian in the Petrofac Training Cup first round on Saturday at Easter Road.
The 22-year will become Mark Warburton’s seventh signing since taking charge of the Ibrox outfit.