The award was recently introduced to honour players who have spent their entire careers with one team.
Le Tissier flew over to attend the Basque derby between Athletic and Real Sociedad and was introduced to the San Mames crowd at half-time.
"It certainly was a big surprise and a very pleasant one too," he told Athletic's official website
"I am incredibly proud to be the first to receive this award.
"My main reason (for staying at Southampton) was my personal happiness and contentment, something which I have always put first among other things.
"That and the fact that I felt a loyalty to pay back Southampton for giving me the chance to achieve my dreams."
Le Tissier scored 209 goals during a 16-year career with the Saints before retiring in 2002.
"For us, what we value most are your (Le Tissier's) values and principles, your loyalty to the same club during your entire career," Athletic said on their website.
"We see ourselves very much reflected in this value and in these principles
For this reason, it is a true honour for us to give you our first One-Club Man Award
This way you will always be part of our history."
Source : PA