Italian Molinari, who along with brother Francesco was part of Europe's thrilling 2010 triumph over the United States at Celtic Manor, took one of the three Open spots available from the tournament at the Fota Island Resort in County Cork.
The other two Open qualifying spots up for grabs at the Irish event were taken by English duo Matthew Baldwin and Danny Willett after both finished tied for third.
Willett posted a hole-in-one on his way to a course-record 63 in the third round on Saturday.
Molinari, 33, said he was delighted to earn a place at the 143rd Open, which will be staged at Hoylake near Liverpool, having endured two operations on his left wrist since his appearance at the 2012 U.S. Masters.
"It is very exciting that after two years with an injury and all sorts of problems that I will be back to play this major especially now that I'm hitting the ball probably the best I've ever hit it," Molinari said in a statement issued by Open organisers the R&A.
"I played Royal Liverpool in my last event as an amateur so it has a special place in my heart."
The Irish Open is the fifth stage in the Open Qualifying Series which continues at the Quicken Loans National on the U.S. PGA Tour next week.
(Reporting by Martyn Herman, editing by Tony Jimenez)
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