"Throughout the tournament, as well as in the final against Portugal, he showed leadership quality and skill and technical ability as well as his character," said French coach Gerard Houllier, a member of the UEFA panel and the former Liverpool manager.
A hard-working midfielder Zagorakis was also named man of the match for the final which completed a remarkable success for Greece, who had been 80-1 outsiders before the tournament.
Zagorakis will be presented with his trophy at a gala in Monaco on August 26.
Eurosport.com XI of Euro 2004
The 32-year-old AEK Athens midfielder was one of five Greek players named in an 'All-Star Squad' by the panel.
Goalkeeper Antonios Nikopolidis, who kept three clean sheets in the knock-out stage, was selected along with the Czech Republic's Petr Cech as one of the two goalkeepers in the squad.
Greek centre-half Traianos Dellas and right-back Georgios Seitaridis featured among the seven defenders while Zagorakis was in midfield and Sunday's goalscorer Angelos Haristeas was one of the forwards.
UEFA All Star Squad:
Goalkeepers: Petr Cech (Czech Republic), Antonios Nikopolidis (Greece)
Defenders: Sol Campbell (England), Ashley Cole (England), Traianos Dellas (Greece), Olof Mellberg (Sweden), Ricardo Carvalho (Portugal), Georgios Seitaridis (Greece), Gianluca Zambrotta (Italy)
Midfielders: Michael Ballack (Germany), Luis Figo (Portugal), Frank Lampard (England), Maniche (Portugal), Pavel Nedved (Czech Republic), Theodoros Zagorakis (Greece), Zinedine Zidane (France)
Forwards: Milan Baros (Czech Republic), Angelos Haristeas (Greece), Henrik Larsson (Sweden), Cristiano Ronaldo (Portugal), Wayne Rooney (England), Jon Dahl Tomasson (Denmark), Ruud van Nistelrooy (Netherlands)
Zagorakis released by AEK Athens
Santini successor to be named on Friday