Halpin, who has twice won the British Society of Magazine Editors' Editor of the Year award, is the first major editorial recruitment by IPC SouthBank managing director Jackie Newcombe since she took on the role in January.
Chunn left In Style in March to edit NatMags' Good Housekeeping. She had edited the magazine since its launch five years ago.
Newcombe said: "[Trish] has enjoyed terrific success with Red and she is the perfect editor to build on In Style's success in the UK.
"The whole team here is thrilled that at a time when In Style is celebrating its fifth birthday, we can welcome someone of Trish's stature and reputation to take the magazine on to its next stage of development."
In Style currently trails Red in the ABC figures on 196,857. Red has a circulation of 219,689.
Founded by Time Inc in the US in 1994, In Style has 10 editions globally and launched in the UK in 2001. The title won the PPA Consumer Magazine of the Year in 2004.
Halpin said: "I have always enjoyed In Style's unique approach to fashion and celebrities and am thrilled to be part of such a major international brand."
In Style is marking its fifth birthday with an invitation-only party at the Victoria & Albert Museum on June 19.
Halpin is a former deputy editor of Emap's New Woman and prior to that worked on Emap teen title More.
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