Cortese was understood to be considering his position at St Mary's over differences with the trust that runs the club, and manager Mauricio Pochettino said on Friday that he would follow him if he decided to leave.
But the Italian met with owner Katharina Liebherr on Friday and plans for the club's continued development in the Premier League were agreed, prompting a statement on the club's official website.
Cortese said: "We are now in a position to move forward with our ambitious plans for the club and I would like to thank Katharina for the very helpful manner in which she approached our talks about long term strategy. I am pleased that this matter is now resolved.
"We can now focus 100 per cent on our preparations for next season.
"We have tremendous momentum now at the club and we are looking forward with great confidence to an exciting and successful campaign next season.
"The last few days have shown me the unity that we now have across the club in the players, the manager, the staff and the chairmanship which normally takes years to achieve.
"I have always believed that to create this unity would make us a very strong club and it is a unity of which I am unashamedly proud."