Radio 4 has attracted 100,000 new listeners following the major overhaul which saw 53 new programmes introduced at the beginning of April.
Quarterly figures from Rajar, the radio industry audience research body, show that Radio 4 increased its average weekly audience to 8.25 million in April, May and June. It was the only BBC radio network to increase its audience compared with the first three months of the year.
Mr Boyle's controversial changes to the station attracted accusations of "dumbing down", but were intended both to bring in new listeners and to persuade existing listeners to stay for longer.
He has succeeded in his first task, but average time spent with the station has fallen from 10.8 to 10.4 hours per listener. The BBC claims that the average has fallen because new listeners are still finding their way around the station.
Mr Boyle said yesterday: "I am really pleased with the vote of confidence in the new schedule. We've extended the reach of the station at a time when a lot of people were watching the World Cup. We've got them in and now we've got to make them stick around for longer and we will tweak the programmes. But it looks as if the basic schedule strategy has worked."
Early analysis of the figures shows that the greatest improvement has come in parts of the day when the station has traditionally been weak, such as the afternoons and evenings.
The controversial decision to move Yesterday in Parliament on to the long wave version of Radio 4 has given the 8.30am to 9.00am segment of the Today programme a slight boost in the ratings.
However, moving the 9.00am news bulletin into the Today programme and starting new shows at 9am has not stopped the major fall-off in listeners when the flagship current affairs programme ends.
"The 9.00am slot is pretty flattish," said Mr Boyle. "That is what we expected, because there was a huge number of new programmes so we have to look at what has worked and what hasn't."
Moving Woman's Hour forward to 10.00am has given the programme a bigger audience and given the hour between 10.00am and 11.00am its biggest ratings.
The BBC is also claiming a success in moving the Archers from 1.40pm to 2.00pm. More than 90 per cent of the afternoon's 1.1 million Archers audience has moved with the show.
The evening episode of the Archers and the Sunday omnibus are now getting slightly higher audiences so Radio 4 believes listeners who cannot catch the afternoon programme are now listening to the repeats in the evening or at weekends.
Even better, from the BBC's point of view, the 2.00pm Archers audience is now staying with the station to listen to its new afternoon dramas, which replaced poorly performing shows such as Afternoon Shift and Kaleidoscope. The relocation of programmes such as the Moral Maze has helped to lift evening ratings, although the BBC concedes it was starting from a low base.
The Saturday morning schedule which saw the most change, with shows like John Peel's Home Truths and a new time for the Food Programme, has seen little change in its audience, but the BBC says it is grateful not to have lost any listeners due to the changes.