Photos were taken near a Christmas tree at a security checkpoint.
Acosta, who was wearing jeans and a sweater, says he was speechless and thrilled by the wedding Moore planned.
Moore says she and Acosta "spent half our relationship in airports."
The couple got a marriage license last week and planned to tie the knot this month, at a site to be determined.
Moore and Acosta met in 2008 in Dallas, where she lived and he was on a business trip. They plan to live in Toledo.