Once you marry, and he files a proper I-485, he will be authorized to stay in the US until the I-485 is either approved or denied. His past overstay is not an issue if you are a US citizen as shown below:
https://www.uscis.gov/policy-manual/volume-7-part-b-chapter-8
B. Immediate Relatives
Certain adjustment bars do not apply to an immediate relative, including the spouse or child (unmarried and under 21 years old) of a U.S. citizen, and the parent of a U.S. citizen older than 21.[2]
An adjustment applicant applying as an immediate relative may be eligible to adjust status even if:
The applicant is now employed or has ever been employed in the United States without authorization;
The applicant is not in lawful immigration status on the date he or she files the adjustment application;
The applicant has ever failed to continuously maintain a lawful status since entry into the United States;
The applicant was last admitted to Guam or the Commonwealth of the Northern Mariana Islands (CNMI) as a visitor under the Guam or CNMI Visa Waiver Program and is not a Canadian citizen;
The applicant was last admitted to the United States as a nonimmigrant visitor without a visa under the Visa Waiver Program; or
The applicant has ever violated the terms of his or her nonimmigrant status.