The other three were Japanese duo amateur Hideki Matsuyama, Daisuke Maruyama and China's Wu Ashun.
Anirban Lahiri, who went through to the Open via the IFQ last year, was the best Indian at tied 23rd with rounds of 73 and 68. Himmat Rai (73-71) was tied 41st and Gaganjeet Bhullar (74-76) was further behind.
Thai rising star Kiradech topped the two-day qualifying with a flawless nine-under 63 while amateur Matsuyama, a two-time Asia Pacific Amateur Championship winner, finished four shots back following a 69 at the Amata Spring Country Club.
Overnight leader Siddikur agonisingly missed out on the top-four spots after sending his tee shot into the water on the par-three 17th for a double bogey.
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Kiradech, nicknamed 'Asia's John Daly' for his grip-it and rip-it style of play, turned in an impressive 30 and added three further birdies to join countrymen Thaworn Wiratchant and Thongchai Jaidee at Muirfield from July 18 to 21.
"I'm glad I achieved my first dream in golf which is to play in a Major championship. I want to do my best at The Open. It will be the biggest challenge and event in my life," said the 23-year-old, who totalled 13-under 131.
It will be his third appearance in a Major tournament after playing in The Masters in 2011 and 2012.
Maruyama, a two-time Asian Tour winner, made an impressive charge up the leaderboard with a round of eight birdies and one bogey to qualify for his first ever Major championship.