The Shulchan Aruch (OC 489:1) rules as follows:
כיצד ביום הראשון אומר היום יום אחד (בעומר) עד שמגיע לשבעה ימים ואז יאמר היום שבעה ימים שהם שבוע אחד (בעומר) וביום שמיני אומר היום שמונה ימים שהם שבוע א' ויום א' (בעומר) וכן עד שיגיע לארבע' עשר יאמר היום ארבעה עשר ימים שהם שני שבועו' (בעומר) ועל דרך זה מונה והולך עד מ"ט יום:
How is this? On the first day, he says, "Today is one day in the Omer," [and so on] until he reaches seven days, and then he says, "Today is seven days, which are one week in the Omer." On the eighth day, he says, "Today is eight days, which are one week and one day in the Omer." Likewise until he reaches fourteen, [when] he says, "Today is fourteen days, which are two weeks in the Omer." In this manner he counts and continues until forty-nine days.
Why do we counts using cardinal numbers, "Today is seven days," "Today is eight days," "Today is fourteen days"? Why not count with ordinal numbers, "Today is the seventh day, which concludes one week of the Omer," "Today is the eighth day, which concludes one week and one day of the Omer"?