The BBC will broadcast more than 3,000 hours of coverage, including 550 hours of television on BBC One and BBC Four.
BBC Radio 5 live and 5 live sports extra will have full coverage of the Olympics (5-21 August) and the Paralympics (7-18 Sept).
Up to 24 live HD video streams will show every moment online.
Fans will also be able to personalise their Rio 2016 experience on the BBC Sport website and in the app.
'My Sport' will enable audiences to follow their favourite sports, signing up for the latest news alerts, setting event reminders and sharing their favourite moments across social media.
Redgrave won rowing gold medals at five consecutive Olympics from 1984 to 2000, while Chris Hoy is the most successful British Olympian of all time with six cycling golds from 2004 to 2012.
"The BBC's coverage of London 2012 was the most watched TV event in UK broadcasting history and we are committed to bringing the same high quality, in-depth coverage to Rio 2016," said Barbara Slater, director of BBC Sport.
"The incredible offering across all our platforms will deliver every moment of the Games through a truly interactive, personalised experience while at the same time fully immersing audiences in this iconic sporting event just as we were so proud to do four years ago."
TV and radio coverage starts with the opening ceremony on 5 August, with live action from 12:00 BST until 04:00 every day until the closing ceremony on 21 August.
The BBC Breakfast sofa, which will move into the home of BBC Sport at MediaCityUK during the Games, will offer extended daily highlights from 06:00.
Baroness Tanni Grey-Thompson, who won 11 Paralympic gold medals, will be part of the Radio 5 live and 5 live sports extra team which provides more than 80 hours of live coverage of the Paralympics.
Along with Redgrave and Hoy, American sprinting legend Michael Johnson - winner of four Olympic golds - and some of Britain's most decorated sporting figures will provide expert opinion and insight into the 28 Olympic sports at Rio 2016.
The line-up across radio and TV also includes former Olympic heptathlon champion Denise Lewis, two-time Olympic cycling gold medallist Victoria Pendleton, marathon world record holder Paula Radcliffe and England's Rugby World Cup-winning coach Sir Clive Woodward.
Double Olympic swimming champion Rebecca Adlington, 2004 sprint relay gold medallist Darren Campbell, three-time world champion gymnast Beth Tweddle and Anthony Joshua, the newly crowned IBF world heavyweight boxing champion, will also be part of the BBC team in Brazil.
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Olympic legends Sir Steve Redgrave and Sir Chris Hoy will be part of the BBC team offering comprehensive coverage of Rio 2016.