This marks the first time that the Rupert Murdoch-owned papers have removed the online paywalls since they were set up for non-subscribers in July 2010.
The barrier was taken down on February 22 this year, but just for the final report of Marie Colvin, the veteran war reporter who was killed while working in Syria.
News International - owner of The Times and The Sunday Times - charges from £2 per week for web-only access, or up to £6 a week for seven days of newspapers with internet and tablet access.
The Sunday Times iPad app will also be available for a free trial, according to a press release.
News International said that The Times and The Sunday Times websites will "feature a range of special Jubilee content, including interactive graphics and video specials, pageant boat spotter guides, photos of the Queen from the past 60 years and live updates from journalists covering the celebrations".
The opening up of the websites also marks "the culmination of a three-week editorial and marketing Jubilee campaign", said the publisher.
Also planned in the campaign is a major street sales operation across London this weekend to capitalise on the big crowds expected to celebrate the Jubilee.
Editorial elements include a "boat spotter" guide for the Thames river pageant, along with a collectable set of commemorative posters.