The 52-year-old, senior manager at the German Federal criminal police office (BKA) and a former Interpol director, will replace Australian Chris Eaton who announced his resignation two weeks ago.
Football's governing body said it would also be beefing up its security department to confront the match-fixing threat.
"Mutschke will be... responsible for all security matters related to FIFA competitions across the world, the global security concepts for football in general, security around FIFA headquarters in Zurich, the FIFA president and the FIFA administration, as well as for matters related to the integrity and protection of the game itself," said FIFA in a statement.
Mutschke, who has more than 30 years' experience at the BKA, faces a huge task after his predecessor warned that the criminal gangs behind match-fixing are infiltrating football by setting up youth and refereeing training academies and buying clubs.
"For me, the main issue will be the integrity of FIFA competitions," said Mutschke.
"The focus here will be on match-fixing, betting fraud and corruption. The initiatives that FIFA has already launched are good steps in the right direction.
"I will now have to pursue these initiatives stringently but also build upon them and implement them consistently with the involvement of Interpol and national security authorities."
His predecessor Eaton travelled the world in the last year leading the campaign against the rigging of games, which is usually orchestrated by illegal gambling rings.
Eaton called for greater co-operation from governments and police, saying that match-fixing is the work of organised criminal gangs which football's authorities cannot take on alone.
Under Eaton's leadership, FIFA offered an amnesty to players who have been involved in match-fixing to come forward with evidence. FIFA also set up a 10-year agreement with Interpol.
Between 50 and 60 matches are currently being investigated by FIFA over possible irregularities.
One of the most high-profile fixtures to come under the microscope last year was Nigeria's 4-1 friendly win over Argentina while Bahrain's 10-0 win over Indonesia in midweek is being probed.
"We have decided to strengthen the former security department, making it into a full division in order to continue to tackle all issues related to football security and the protection of the integrity of the game," said FIFA secretary-general Jerome Valcke.
"This is another major step in our determination to ensure a clean and safe sport and to underline our commitment to the fight against match-fixing in football."
