The show - which runs from 6.30 to 9.30am on weekdays and also features Moira Stuart, Lynn Bowles and Vassos Alexander, has added 16,000 listeners on the same quarter last year 9.75m last year and 8,000 from the first quarter of the year.
The standout performance makes the 48-year-old the most popular radio host since the current Rajar listening methodology began in 1999.
Evans has presented the show since January 2010, when he took over from Sir Terry Wogan, who bowed out with 8.1 million listeners.
Evans is now almost 4 million ahead of his Radio 1 breakfast rival Nick Grimshaw, who also recorded a rise during the second quarter to 5.97 million – up from 5.89 million this time last year.
Helen Boaden, director of BBC Radio, said: "Chris is a brilliant presenter and a unique talent. The Radio 2 Breakfast Show is unlike anything else on radio, with great music, news, sports updates and Pause for Thought alongside features like the 500 Words children’s writing competition, and shows that utterly distinctive, high-quality programmes can also attract large audiences."
The figures – which cover the period from 31 March to 22 June - show all BBC Radio has a weekly reach of 35.23 million, compared to last quarter’s 35.31m and last year’s record 35.88m, and a share of 53.3% – down from 54.9% last quarter and 53.9% last year.
BBC Radio 3 has a weekly audience of 1.88 million listeners, compared to 2.0m last year and 2.09m last quarter, and the network’s share is 1.0%, from 1.2% last year and 1.3% last quarter.
BBC Radio 4 posted a weekly reach of 10.53 million during the period, from 10.98m last year and 10.95m last quarter. Its share of listening is 11.6%, compared to 12.2% last quarter and 12.1% last year. The Today programme has 6.71 million listeners each week, from 6.97m last year and 7.06m last quarter.
BBC Radio 5 live recorded a weekly reach of 6.28 million, compared to 6.04m last year and 6.17m last quarter. Its share is 4.1%, level with last year and last quarter.