The trio took the three places available in the Open Championship to players finishing in the top 10 at Royal County Down, who were not already exempt.
Kjeldsen claimed his spot with victory in a three-man Irish Open play-off ahead of Pepperell and Austria???s Bernd Wiesberger, who had already booked his place at St Andrews.
“It’s like I am dreaming but I don’t want anyone to wake me up,” Kjeldsen said, who has not played in the Open since it was last held at St Andrews in 2010. “Three weeks ago I was 112th in the Order of Merit and my game was not in good shape.
???With turning 40 (a fortnight ago) you wonder was that it? Now I am standing here and it’s pretty remarkable really.”
Kjeldsen, whose last win came in the Open de Andalucia in 2009, saw a two-shot overnight lead slip away on multiple occasions during the final round, before securing a fourth European Tour title with a birdie at the fourth extra hole.
“The last breath I took was on about the 14th,” Kjeldsen added. “I have never been as nervous as this in the other tournaments I have won.
“I had decided not to look at leaderboards but once I started dropping shots I started looking, because it gave me a little pleasure that I wasn’t the only one struggling.
“I was leaking shots left, right and centre but made a great up and down on 15 and the three-wood second shot in the play-off was pretty special.”
Spain’s Rafael Cabrera-Bello missed out on the play-off – and with it a place in the Open – after a bogey on the 18th, with Hatton alongside Cabrera-Bello on one under after a par on the last in a closing 74.
Hatton took the third qualification place due to having a superior world ranking than Cabrera-Bello, while a career-best European Tour finish this week for Pepperell means he???ll make his Open debut this summer.
“It’s great. It didn’t cross my mind until I walked off the 18th and my caddie told me,??? Pepperrell said. ???That’s a real bonus. I know my dad and a few friends had already planned to go there regardless.
“Having never played an Open before, for my first one to be St Andrews is going to be quite special and the fact that we play there every year (in the Dunhill Links Championship) can only help. I’ll go there pretty confident.”