The news was read out live on the Radio 2 Breakfast Show on Thursday, which was guest hosted by Sara Cox.
On Wednesday’s show, Evans had called his wife, Natasha Shishmanian, to check up on her ahead of her labour being induced later that day, and the twins were born hours later.
The statement, read out on air, said: “Ping and Pong arrived safe and well last night. Ping popped her head out at 22.10, Pong popped his head out 12 minutes later at 22 minutes past 10. Both healthy, both strong, happy and blessed, as was mum throughout.
“Infinite thanks to the amazing team at Frimley Park Hospital, amazing people, amazing professionals, helping dreams come true. Thank you.”
Last week, Evans said Ping and Pong was a “working title” for his babies, and that he was considering using them as middle names.
He told Janet Jackson, a guest on his Breakfast Show: “We call them Ping and Pong because they are the unborns. We have a working title!”
But he added: “It’s so cute I want to keep them as the names Ping and Pong.”
When singer Jackson asked whether he meant nicknames, Evans replied: “Or middle names.”
At the beginning of the show, Cox joked she was the new host.
Cox is rumoured to be in the running to replace Evans, who is leaving the flagship programme to return to Virgin Radio, though Zoe Ball has reportedly been offered the job.
As she introduced the programme in Evans’ absence on Thursday, she said: “Well here we are then, welcome along to the show. My name is Sara Cox, we never thought we would get here, this is your brand new Radio 2 Breakfast show and I just want to say I am so thrilled. I would like to thank my mum for her support...”
She then broke off and could be heard speaking to someone in the background, saying: “Just one day? Oh.” The show then cut to music.
Evans and Shishmanian married in 2007. As well as the twins, they also have sons Noah, nine, and six-year-old Eli.