Born in Lausanne, Celestini started playing professionally with hometown club FC Lausanne-Sport, then had a four-season spell in France, spending two years each with Troyes AC and Olympique de Marseille.

[3] After the team's immediate relegation he stayed in the country, joining fellow La Liga club Getafe CF where he never was an undisputed starter, but managed to feature heavily in consecutive seasons.

[4] On 16 February 2010, after having been regularly used in the past two seasons, albeit not as a usual first-choice, the 34-year-old Celestini announced he would not renew his contract with Getafe, choosing to return to Lausanne on a one-year deal.

A Switzerland international since 1998, Celestini collected 35 caps and was a participant at the UEFA Euro 2004 (appearing in two incomplete matches, as the nation exited in the group stage).

[6][7] On 24 March 2015, after a spell as assistant manager at Spanish club Málaga CF[8] and head coach with Italian amateurs Terracina Calcio 1925,[9] Celestini replaced Marco Simone at Lausanne-Sport in the latter capacity, as the side was in a poor run of results in the Swiss Challenge League.