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The ex-Switzerland international plans to stand in the election on March 18, 2027, in Rabat, Morocco.
Vega, who enjoyed a memorable spell at Celtic during the 2000/01 Treble-winning campaign under Martin O'Neill, launched his candidacy with a statement demanding significant changes in world football governance.
The 55-year-old stated: "Football belongs to the people," as he expressed his wish to restore faith in the sport's governing body.
Vega said: "After more than a decade of preparation, I formally announce my candidacy for the Presidency of FIFA in 2027.
"I bring the mentality of a player, the discipline of a defender, and decades of experience from the pitch to the boardroom.
"I defended my team on the field. Now I am ready to defend football itself, its integrity, its people, and its future."
Vega emphasised that his campaign was not driven by "personal ambition, power or privilege," but rather as a push for reconciliation and fundamental change within world football.
"This is not merely an announcement of candidacy. It is a call for fundamental change, a commitment to reconciliation, and a vision for a new era of world football."