President Massimo Moratti originally resisted bringing in Sneijder, but the move went through on the final day of the transfer campaign.
"Of course I will stay, I am not thinking of leaving this club. We just finished a great season and won three titles, the biggest thing that can happen in your football life. Now we are all enjoying it.
"From when I joined Inter I wasn't thinking of the Treble, but when we started playing together I believed in it, as we have an amazing team. We fight together, win together and play great football.
"This wonderful mixture has taken us to the Final and we deserved to win. The supporters were all with us from the first moment and I want to give a big kiss to the fans."