Aulas claimed Essien is staying as new boss Gerard Houllier signed striker John Carew from Besiktas in a £5m deal.
He said: "I have always said that Essien and Mahamadou Diarra will stay. There were a lot of frustrating rumours for me."
Chelsea are reported to have had a £16.75m offer for 22-year-old Essien turned down by Lyon.
Aulas wants to build Houllier's new side around Essien and Diarra and said: "I confirm that they will stay, as well as Juninho. Having all of them in our team makes it stronger than before."
He added: "The best recruitment starts by keeping the team's best players, and that's what we've done."
Carew, 26, has signed a four-year contract after also having spells playing for AS Roma in Italy and Valencia in Spain.
"We had talks on Saturday and then all Sunday with the player and Besiktas management," said Aulas.
"It's great news for Lyon. He has been one of the club's priorities for several seasons but we were never able to see it through.
"We are very happy with the conclusion. He will boost the squad wth so much power and speed."
Houllier said: "For us it's a chance to take him and for him an opportunity to rebound after two or three average seasons on his part."