GlaxoSmithKline is selling the historic brands to Japanese drinks group Suntory Beverage & Food after putting them up for sale earlier this year.
Lucozade and Ribena, which date back to 1927 and the 1930s respectively, are made in the UK at a factory in Coleford, Gloucestershire, which employs around 500 staff.
Drugs giant Glaxo kicked off their sale in April after concluding they would grow better under a different owner. Instead it plans to increase the focus of its consumer healthcare business, which includes brands such as Sensodyne, Panadol, Aquafresh and Nicorette.
Lucozade is the UK's top-selling energy and sports drink, while blackcurrant drink Ribena is the fourth-best selling fruit juice and concentrate.
Glaxo chief strategy officer David Redfern said Lucozade and Ribena have made a huge contribution over the years, and their future is in "good hands".
He said: "Now is the right time to sell them as we increase the focus of our consumer healthcare business and execute the delivery of our late stage pipeline of pharmaceuticals and vaccines."
The drinks were owned by Beecham prior to its merger with SmithKline, and more than three-quarters of their sales are in the UK. They earn annual revenues of about £510 million a year. The drinks are also produced in Nigeria and Kenya.
Suntory, which bought Orangina in 2009, said the brands will help it grow faster in the UK and expand to become the leading global soft drink company by 2020.
The cash deal is expected to complete by the end of the year, subject to regulatory approval.
Suntory Beverage & Food, which is part of the £12 billion turnover Suntory Group, said the drinks' sales networks will help it grow its other brands in countries such as Nigerian and Malaysia.
The brands are said to have attracted considerable interest from private equity groups including CVC Capital Partners and KKR, and were also reportedly in the sights of Irn-Bru owner AG Barr.
In the three months to the end of June, Lucozade sales grew 4% but Ribena was down 2%.