The 1958–59 season was the club's 40th official season and their 56th year in existence. The club participated in the final season of the
Istanbul Football League finishing in 5th place, behind
Fenerbahçe,
Galatasaray,
Karagümrük and
İstanbulspor. By finishing in the top 8, the team qualified for the inaugural season of the new national league;
Turkish First Football League. By winning the
Turkish Federation Cup a season ago Beşiktaş qualified for the
European Cup, but lost to
Real Madrid 1-3 on aggregate (0-2 away, 1-1 home) in the first round. Real Madrid however would go on to win the cup for a 4th time. Beşiktaş was placed into the "White Group" along with
Fenerbahçe,
Altay,
Izmirspor,
Ankaragücü,
Hacettepe,
Beykoz and
İstanbulspor. Beşiktaş finished 2nd place behind Fenerbahçe missing the final match, where Fenerbahçe would beat Galatasaray for the title.
In the first season of the
Turkish First Football League (now Turkish Super League), Beşiktaş finished 2nd behind Fenerbahçe, thereby failing to qualify for the final.
Beşiktaş became the first Turkish team to qualify for the European Cup. They qualified in 1957 but the
Turkish Football Federation didn't send their name for the draw, therefore being disqualified.
They beat
Olympiacos F.C. in the preliminary round by a w/o because Olympiacos withdrew from the competition. In the first round they played the defending champions
Real Madrid. In the first leg Beşiktaş lost 0-2 and in the second leg they tied 1-1. Real Madrid won 3-1 on the aggregate.