She replaces Louise France, who left to edit the Sunday broadsheet's Review section in June after two years on the title.
Formerly assistant editor of OM, Kenny takes up her new role this month.
She will report to OM editor Allan Jenkins.
Neither Kenny nor Jenkins were available for comment on her promotion.
It is thought an assistant editor to replace Kenny is on the point of being hired.
OM, previously called Life, was revamped earlier this year (PRWeek, 12 April). Ian Tucker was hired as commissioning editor in March from a background in entertainment magazines. The idea behind the relaunch was getting shorter pieces into the title, although the mixture of columnists, arts, reportage and lifestyle has remained.
Pagination has increased and the paper's TV guide was increased to A5 size at the same time.
Observer Sport Monthly and Observer Food Monthly - both launched in the past two years - have also received widespread acclaim.