The BBC has reached a deal with the International Olympic Committee (IOC) over the international streaming of some of its radio shows.
The Today Programme on Radio Four was unavailable to listeners outside the UK on Friday, as it was broadcast from inside the Olympic park.
Overseas listeners can normally tune in live on the internet or on iPlayer.
The IOC, which holds international broadcast rights from Olympic venues, will now allow access to some shows.
Restrictions had been placed on Chris Evans' Breakfast Show as it is being broadcast from the Olympic park in east London for the duration of the games.
However, following discussions between the BBC and the IOC, it has been agreed that there is no need to block international streams of certain shows, including Radio Two's popular breakfast programme.
Radio Four programmes with a wide news agenda will also be free to broadcast to international listeners.
All programmes on Radio Five Live - except the news programme Up All Night - will remain available only in the UK as they will be devoted to the games.
Mark Friend, head of online services for BBC Audio and Music said: "Unfortunately there are some types of content where we are restricted from distributing overseas, usually because of sports rights.
"The impact of this will be very noticeable throughout the Olympic games because the BBC has the rights to broadcast from Olympic venues only to the UK."
In some cases, when only sections of shows are broadcast from an Olympics site, the BBC said it may be possible to block the Olympics segment and make the rest of the programme available to international audiences.
However, programmes featuring substantial amounts of Olympics content will be blocked, as there are not sufficient resources to edit them.
When an entire programme or a shorter segment is unavailable to overseas listeners, they will hear a message informing them of the rights restrictions in place.