Ofoborh put pen to paper on a four-year deal with the Gers, but he will team up with them in the summer.
The midfielder is currently on loan at Wycombe Wanderers, but he will switch to the SPFL at the end of the current campaign when his contract with Bournemouth expires.
Speaking on his signing, Sporting Director, Ross Wilson, commented: “We look forward to welcoming Nnamdi to our group in the summer. We are extremely impressed by his qualities and he is a player that has real progression in him.
“He has a positive and determined personality and is very much looking forward to becoming a Rangers player at the end of this season.”
Nnamdi Ofoborh will become the third Nigerian at the club after Joe Aribo and Leon Aderemi Balogun.