The football team plays its home games at the Estadio Osvaldo Domínguez Dibb, also known as "El Bosque" (The Forest) and "Para Uno".

The act of foundation was written in the Rodi's family home, located in the streets of Azara and Independencia Nacional in downtown Asunción, Paraguay.

The final decision came to William Paats who chose "Club Olimpia" as the team official name, in honor of the Greek city of Olympia where the Olympic Games were born.

After the unpleasant times in the 1940s decade Olimpia started to establish its dominance in the Paraguayan league when Manuel Ferreira Sosa assumed the presidency of the club in the mid-1950s.

[4] The club also had a first taste of international success in 1960 in the first edition of the Copa Libertadores de América by reaching the finals in which they lost to Peñarol.

Ironically, the winning goal for Peñarol in the finals was scored by Uruguayan Luis Cubilla, who later became a coach and led Olimpia to several national and international championships.

The new president hired coach Luis Cubilla, who led Olimpia to its first international cup title when the club defeated Boca Juniors of Argentina in the 1979 Copa Libertadores finals.

That result allowed Olimpia to play their effective defensive scheme in the famous La Bombonera stadium in the second leg, ending the match in a 0–0 draw that gave the Paraguayan side its first Copa Libertadores.

For that matter, the club's president, Osvaldo Dominguez Dibb, decided to make a financial effort to bring Raul Vicente Amarilla, a Paraguayan striker that had proven his quality in the Spanish league over the years.

The signing of Oscar Amarilla was as positive for Olimpia as expected, as the team reached the 1989 Copa Libertadores finals but came up short, being defeated by Atlético Nacional.

This way Olimpia obtained its second Libertadores Cup with a 3–1 aggregate scoreline and a formidable team that had key players such as Almeida, Gabriel González, Samaniego, Amarilla among others.

Not content with the Libertadores title itself, Olimpia went on to win the 1990 Supercopa Sudamericana, a tournament reserved only for the best teams in South America.

In that same year, Olimpia played the Intercontinental Cup final in Japan against the European champion AC Milan, losing 3–0.

The achievement of all the mentioned international titles in 1979 and 1990 established Olimpia as one of the most respected and traditional teams in South American football.

Amongst other trophies won by Olimpia at the time, the club were crowned undefeated champions of the 1992 Torneo República, with Roberto Perfumo as team manager.

Olimpia's base formation for the tournament was with Ricardo Tavarelli in goal; Néstor Isasi, Julio César Cáceres, Nelson Zelaya and Henrique da Silva in defense; Sergio Orteman, Victor Quintana, Julio Enciso and Gastón Córdoba in midfield; and Miguel Benítez and Richart Báez (later Hernán Rodrigo López) in the front.

A fourth-place finish in the annual table (adding both Apertura and Clausura tournaments) allowed Olimpia to return to international play after 4 years of absence with the 2008 Copa Sudamericana.

A very important fact of this new era of the Olimpia, is that number of active fan members of the club was triplicated just in three months, and that they are still increasing because of the team's great performance.

[citation needed] But then again, in the second round of the tournament, a dispute emerged among the chairman, the coach and some of the players, as Marcelo Recanate accused them of "not giving all his finest efforts in the field".

[12] The title came after defeating Rubio Ñu 2–1 at the Estadio Defensores del Chaco and finishing three points ahead of Cerro Porteño.

The title was largely celebrated by energetic fans on the streets of Asuncion and nearby cities due to the way it was won with Olimpia having only a one-point lead over rivals Cerro until the last matchday.

In the 2012 Apertura Olimpia finished in second place in the Primera División, and qualified for the 2013 Copa Libertadores along with the two other big teams of Paraguay, Cerro Porteño and Libertad.

[20] National International Olimpia has an athletics department directed by Ronaldo Almiron and participates in the competitions of the Federación Paraguaya de Atletismo.