Atletico claimed their first Spanish league title in 18 years after earning a 1-1 draw at fallen champions Barcelona on Saturday.
Diego Simeone's men finished three points clear of powerhouses Barcelona and Real Madrid.
The Madrid-based outfit are also set to contest the UEFA Champions League final against city rivals Real in Lisbon on Saturday.
And Gabi believes Atletico are about to embark on a sustained period of success under the guidance of coach Simeone, who played for the club the last time they won the La Liga title in 1995-96.
"Thank you very much to everyone," Gabi told fans during Atletico's victory parade in the Spanish capital.
"For me it is an honour to be here and to share a dressing room with these people and achieve what we have achieved.
"It is a reward for hard work and sacrifice, and for the love we have for our colours that you can't buy.
"We are only just beginning."
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