The appointment of the low-profile 43-year-old Dudamel, who played 54 times for Venezuela, rather than a world-renowned coach reflects the governing body's lack of cash.
He spent a large part of his playing career in Colombia and most recently coached a minor club side in Venezuela.
Dudamel replaces Noel Sanvincente, who quit this week after a 4-1 home loss to Chile, leaving them bottom of South America's World Cup qualifying section with one point from six games.
The federation said its choice was restricted because its chief sponsor, cash-strapped state oil company PDVSA [PDVSA.UL], did not pay the organisation any money last year amid a severe recession in Venezuela. (http://reut.rs/1qmAlmE)
"If we had the money as per the (sponsorship) contract, of course we could have sought a world-class coach," Laureano Gonzalez, president of the FVF, told a news conference, saying PDVSA was meant to give the federation $8 million.
"(But) the country is in the circumstances that it's in and we cannot bring in a world-class coach from abroad."
However, Gonzalez added that the new manager, who will stay on until 2017, "is young, with a defined personality."
Dudamel, who was not at the news conference, faces an uphill battle to get Venezuela back on track amid the financial troubles.
The top four teams in the South American qualifiers get an automatic place at the World Cup in Russia, while the fifth-placed side go into an interncontinental playoff.
"We've used up our reserves and today the Venezuelan team has to adjust to reality," Gonzalez said.
(Reporting by Alexandra Valencia; Writing by Alexandra Ulmer; Editing by Ken Ferris)
