The 34-year-old Swift racked up his 140th appearance in the league to overtake Cardiff Blues's Deiniol Jones at the top of the pile.
Having joined Connacht in 2000 Swift has racked up a staggering 214 caps in all competitions and has played alongside current head coach Eric Elwood in his time at the Irish outfit.
Swift is one of a select few to have played in the first edition of the Celtic League back in 2001 and is still going strong.
Known for his ferocious tackles and towering lineout presence, the colossal 6ft 5in, 120kg lock admits he has no intention of slowing down just yet.
"I'm obviously over the moon to reach this milestone," he said.
"The league has gone from strength over the years as has the quality of the rugby played so as a brand the RaboDirect PRO12 stands in a great place at the moment."
"I suppose you could put my longevity down to a mix of good fortune and a great medical team looking after me."
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