Algerian Bouhenna has signed a 12-month contract having left French Ligue 2 side Sedan.
Radford, 18, returns to the UK on a five-month contract after being released by Hungarian club Ferencvaros.
Born in Rotherham, Radford began his career at Sheffield United before transferring to the Blades' feeder club in Hungary at the age of 16.
He told the club's website: "I signed for Ferencvaros for two years and matured a lot over there.
"When the opportunity came to sign here, I couldn't let it slip."
Bouhenna, 20, said: "I'm proud to come over to England. The French people admire the English leagues."
Rovers have so far been able to rebuff approaches for their top players, including a £2.3m bid in May from Ipswich Town for striker Billy Sharp and midfielder James Coppinger.