The assaults involve 10 girls aged between nine and 16-years-old and the rape charge concerns a woman aged 22 when the alleged offence took place in 1976.
Lancashire Police arrested Hall earlier on Tuesday after he attended a police station by appointment. He was bailed to appear before magistrates in Preston, northwest England, on February 7.
"Following consultation with the Crown Prosecution Service an 83-year-old man has this evening been charged with one offence of rape and 14 offences of indecent assault," a Lancashire Police statement said.
The presenter pleaded not guilty to three other charges of indecent assault when he appeared in court earlier this month, and will now answer those charges in crown court.
Hall has been a familiar face and voice in British broadcasting for half a century and was last year awarded an Order of the British Empire (OBE).
His eccentric and distinctive football match summaries have made him a cult figure on BBC radio.
Police have stressed that the charges against him are not part of the investigation into allegations of sexual abuse of children against the late BBC star Jimmy Savile.