Once you have married your fiancee who arrived in the US on her K-1 Visa she would have to apply for an adjustment of status after you have married. Your wife who is now a lawful permanent resident is granted the privilege of permanently living and working in the United States. If you want to become a lawful permanent resident based on the fact that you have a relative who is a citizen of the United States or a relative who is a lawful permanent resident, you must go through a multi-step process.

The following might be needed by USCIS :

• Application for Alien Relative (I-130) (not necessary for K-1 applicants);
• Application to Register Permanent Residence (Form I-485);
• Biographical information (Form G-325);
• Medical Exam Sheet is not required, if your Spouse has had a medical exam based in K-1 visa;
• Two color photos taken within 30 days;
• Evidence of inspection, admission or parole into the United States (Form I-94, Arrival Departure Record);
• Affidavit of Support (Form I-864 with supporting documents);
• Authorization for employment (Form I-765)
• Travel Parole (Form I-131)