Out of the 35-player squad he inherited, Antić quickly identified 20 players he was counting on for the following season before setting about adding 5 to 6 more players during the transfer window. That meant the end of Atlético days for a slew of players including aging goalie Abel Resino, embattled Colombian striker Adolfo Valencia, Brazilian Iván Rocha, Polish striker Roman Kosecki, Russian winger Igor Dobrovolski, etc.
First on Antić's wish list was defender Viktor Onopko whom he coached at Real Oviedo: Atlético and the player agreed terms, however, Oviedo management weren't satisfied and the case ended up before FIFA arbitration commission, which ruled in Oviedo's favour. Antić then tried to get 19-year-old Fernando Morientes from Albacete, but the talented striker signed with Real Zaragoza.[13] Out of the players Antić did manage to sign, the biggest find turned out to be unheralded winger Milinko Pantić whom Antić plucked from obscurity in Panionios for very little money. The move initially raised eyebrows with many questioning the usefulness of a complete unknown who is about to turn 29 years of age, however, over the coming season Pantić would prove himself to be the missing piece this team needed with key goals and assists. Another key acquisition was 29-year-old Bulgarian tall centre forward Luboslav Penev, brought in from Valencia despite questions about his health due to a recent bout with testicular cancer. Other incoming transfers included goalkeeper José Francisco Molina and central defender Santi Denia from Albacete, midfielder Roberto Fresnedoso from Espanyol, and young Argentine striker Leo Biagini from Newell's Old Boys who starred at the 1995 FIFA World Youth Championship.
Playing in the domestic league that was just expanded from 20 to 22 teams along with a new points system with three points awarded for a win, under Antić's command, the Atlético squad featuring Molina in goal,Delfí Geli and Santi Denia in central defence, Roberto Solozábal and Toni on right and left back respectively, Juan Vizcaíno (whom Antić previously coached at Zaragoza) and Caminero in centre midfield, Simeone and Pantić on right and left wing respectively, and finally Penev and Kiko upfront gelled together masterfully en route to a historic La Liga/Copa del Rey double in the 1995–96 season. Other players that didn't start as often, but nevertheless contributed significantly throughout the season were Fresnedoso, Juan Manuel López, Biagini, Pirri Mori, etc.
Antić's Atlético began the league campaign in furious fashion with four impressive wins. Once they took the top league spot after week 2, los Colchoneros gave it up only once (after the week 5 scoreless draw at Sevilla), before reclaiming it the very next week and impressively continuing on top until the end with Penev scoring 16 league goals, Simeone 12, Kiko 11, Pantić 10, and Caminero 9. Atlético also featured a stingy defence that allowed 32 goals – less than any other team in the league. Still, the title wasn't secure until the very last match, as Valencia stayed in close pursuit until the end. Going into the last round of matches on Saturday 25 May 1996, Atlético was on 84 points with Alabacete to play at home while Valencia had 82 and Celta away. The victory was never in doubt as Simeone and Kiko scored in the first half sparking off jubilant scenes at Vicente Calderón Stadium.[14]
Month and a half earlier Antić already claimed his first trophy of the season, beating Johan Cruyff's Barça in the Copa del Rey final in Zaragoza after extra time on a goal by Pantić.
Winning the double endeared Antić to Atlético faithful and more importantly to club's controversial president Jesús Gil. Notorious for quickly and impulsively going through coaches, Gil kept Antić at the helm of his team for two more seasons (three consecutive seasons in total) – a record of sorts considering Gil's trigger-happy nature when it came to gaffers.
