Qatar beat Vietnam 4-2 on aggregate in the second round of World Cup qualifiers Asian zone last month but the Qatar Football Association (QFA) said they decided to end the contract after the "rather alarming fashion" in which they edged the "humble" southeast Asians.
Qatar, who have never qualified for the World Cup finals but will host the tournament in 2022, lost 2-1 to Vietnam in Hanoi in the second leg after easing past the 144th FIFA-ranked side 3-0 in Doha.
"We thank him for his efforts. But we feel this is a time to move on so we mutually agreed to end the contract," QFA President Sheikh Hamad bin Khalifa Al Thani said in a statement late on Sunday night.
The first task for the much-travelled Lazaroni will be to ensure the tiny Gulf emirate finishes in the top two of a group containing Iran, Bahrain and Indonesia in order to qualify for the fourth round of Asian qualifying.
Qatar travel to Bahrain to begin their Group E campaign on September 2.
Lazaroni, who was previously in charge of domestic league side Qatari Sports Club, led Brazil at the 1990 World Cup but they exited in the second round after a 1-0 loss to Argentina.
He has also coached Italian clubs Fiorentina and Bari, Turkish side Fenerbahce and had spells managing in Japan, Portugal and Saudi Arabia.
Rajevac guided Ghana to the quarter-finals of the 2010 World Cup in South Africa, where they lost to Uruguay on penalties.
