The overnight leader carded five-under 66 in his final round on the Crans-sur-Sierre course to finish on 16-under par.
Ramsay led by one shot at the start of the day but five birdies in the front nine and an eagle on the 14th was more than enough to claim his first win since the 2010 South African Open. Not even two bogeys on the 13th and 17th could ruin the 29-year-old's day.
Paul Lawrie, who won the Johnnie Walker Championship at Gleneagles last week, was tied for second alongside Danny Willett at the end of the third day.
However, the Scot had to settle for a share of sixth place after a final round score of 70 left him on 11-under with Chile's Felipe Aguilar and Bernd Wiesberger of Austria.
England's Willett remained tied for second on 12-under alongside Sweden's Fredrik Andersson Hed, Marcus Fraser of Australia, and Frenchman Romain Wattel.