כִּֽי־יִקַּ֥ח אִ֛ישׁ אִשָּׁ֖ה וּבְעָלָ֑הּ וְהָיָ֞ה אִם־לֹ֧א תִמְצָא־חֵ֣ן בְּעֵינָ֗יו כִּי־מָ֤צָא בָהּ֙ עֶרְוַ֣ת דָּבָ֔ר וְכָ֨תַב לָ֜הּ סֵ֤פֶר כְּרִיתֻת֙ וְנָתַ֣ן בְּיָדָ֔הּ וְשִׁלְּחָ֖הּ מִבֵּיתֽוֹ׃
사람이 아내를 취하여 데려온 후에 수치되는 일이 그에게 있음을 발견하고 그를 기뻐하지 아니하거든 이혼 증서를 써서 그 손에 주고 그를 자기 집에서 내어보낼 것이요
Mishneh Torah, Marriage
If she gives the money and says, "I am sanctified to you", "I am engaged to you", "I am a wife to you" or any other acquisition term, she is not sanctified. So too if she gives the money and he speaks, she is not sanctified. If he gives and she speaks, this is a questionable sanctification.
Gray Matter III
These authorities explain that Halachah views a woman who marries as moving to a new community — her husband’s home. Rav Moshe cites a number of biblical verses that demonstrate that the Torah views marriage as a woman moving into her husband’s home. For example, the Torah (Devarim 24:1), in describing the procedure for a divorce, states that the husband “shall send her from his home.” We see that the Torah considers a wife to be in her husband’s domain during the marriage. Accordingly, the wife must accept the customs of her husband’s family. Rav Ovadia and Rav Felder also cite the Tashbeitz as a precedent for their ruling.
Shulchan Arukh, Even HaEzer
He says to her, "Hareini, I am your man (Ishecha)," "Hareini, I am your husband (Ba'alech)," or "Your betrothed;" these are nothing, even they were speaking initially about the business of betrothal since it is written, "Since (Ki) He will take..." and not "That (She'Yikach) he will take (through his declaration) for himself." [Rama: Similarly, if he gives the money to a man (her father) and says to him, "Harei, you are my father in-law," and did not say, "your daughter is betrothed to me," here there is also nothing.