Lancashire Police said the alleged offences were committed between 1974 and 1984 and involved three girls aged between nine and 16 years.
Hall, 82 – who presented It's A Knockout and provides football reports for Radio Five Live – was released without charge on an allegation of rape and a further allegation of indecent assault.
The broadcaster has been bailed to appear before magistrates in Preston on January 7.
John Dilworth, head of the Crown Prosecution Service's north-west complex casework unit, said: "Following investigations by Lancashire Police into allegations of sexual assault by Stuart Hall, I have reviewed all the evidence and have authorised Lancashire Police to charge him with three counts of indecent assault.
"The charges are that between September 1, 1974, and December 31, 1974, he indecently assaulted a woman who was then aged 16 or 17 years; that between January 1, 1983, and December 31, 1983, he indecently assaulted a girl then aged eight or nine years; and that between July 1, 1984, and September 27, 1984, he indecently assaulted a girl then aged 13 years."
Hall was detained at his home in Wilmslow, Cheshire, yesterday before being taken to a police station for questioning.
Police officers arrived at his home at about 8am and stayed until about 2pm. A uniformed officer left carrying two bin bags containing items. There were two marked Cheshire Police vehicles in the driveway of his home for several hours.
Hall has been a familiar face and voice in British broadcasting for half-a-century and was awarded the OBE in the 2012 New Year Honours list. His eccentric football match summaries have made him a cult figure on Radio Five Live.
A BBC spokesman said: "In light of the very serious nature of these charges, Stuart Hall will not be working at the BBC while the police continue with their inquiries."
The broadcaster's arrest comes as the embattled corporation continues to deal with the fallout from the Jimmy Savile sex abuse scandal. It is understood the allegations against Hall are not part of the Operation Yewtree investigation into Saville and others.