More than 23,000 tickets have already been sold for the hour-long accompanied tours, organisers said, which offer a sneak preview before the Stratford site begins to open in July.
Visitors don hard hats and high-visibility jackets to tour what is still a construction site, where sporting venues are being transformed into a new district of homes, schools and businesses.
The "Park in Progress" bus trips, offered on weekends and school holidays until June 23, will also include a visit up the red ArcelorMittal Orbit tower designed by Anish Kapoor.
London Mayor Boris Johnson said: "We promised to give people opportunities to get back onto the park as soon as possible and it is no surprise that there is a huge appetite from Londoners for these fantastic tours offering a chance to see this exciting metamorphosis first hand."
Whole sections of the park are being rebuilt with new cafes, community centres and gardens added, as part of a 18-month scheme costing £292 million ($463 million, 348 million euro).
The Riverside Hockey Arena has been dismantled, the largest McDonald's in the world has gone and the temporary seating stands on the Aquatics Centre are being taken down.
The competitors' accomodation is being transformed into almost 3,000 luxurious flats, new homes and schools are under construction and the whole area will be surrounded by a new park.
The Queen Elizabeth Olympic Park reopens in part in July and will re-open fully from next year. Planners hope that within 20 years, the new district will be home to 8,000 people.
It will still host sporting events, however, from football to athletics.
The London Anniversary Games will be held at the Olympic Stadium in July, including the Diamond League athletics meeting expected to attract stars including Jamaican sprinter Usain Bolt.
English Premier League club West Ham United will then become the main tenants of the £429 million ($648-million, 503-million-euro) venue, which hosted the athletics and the opening and closing ceremonies.
The 80,000 capacity stadium will be converted to a 54,000-seater venue in time for the 2016-2017 football season.