Galeone started his coaching career at 34 for Serie D team Pordenone, in 1975/1976, obtaining an eleventh place in his debut season. His first coaching experience in a professional league came in 1978/1979 for Cremonese of Serie C1, but ended with a sacking. After a few other experiences, including three fairly successful seasons at SPAL of Serie C1, in 1986/1987 Galeone signed for Serie B team Pescara, the team whose name is associated with him still today. In his debut season with Pescara, Galeone won Serie B and led his team directly to the first Serie A time ever for his side, and managed to save Pescara from relegation the following season. He left Pescara in 1988/1989, after having failed to avoid relegation for his second time, but returned in 1990/1991 and regained promotion to Serie A in 1991/1992. Other than Pescara, where he coached also in 1999/2000 and 2000/2001, Galeone served as head coach for Udinese Calcio in 1994/1995, obtaining a Serie A promotion, Perugia in 1995/1996, where he obtained his fourth and final Serie A promotion, Napoli in 1997/1998 and Ancona in 2003/2004. In 2006, Galeone made his comeback at Udinese, as he was called to replace Loris Dominissini and Néstor Sensini at the helm of the bianconeri.
Galeone is well known for being a strong advocate for 4–3–3 zonal marking and an attacking style of playing, which made of him one of the most innovative Italian football coaches in the late 1980s alongside Arrigo Sacchi. At 65, he had been the oldest active head coach in the 2006/2007 Serie A, before being fired on January 16 after disagreements with the club.
On July 19, 2007 he was announced to make a fourth comeback at Pescara, this time as technical consultant beside new boss Andrea Camplone, a former player of him in the 1990s, but left the club only one month later.