Guttman, 53, has a reputation for being a methodical and meticulous tactician and was the only candidate considered for the position. He received unanimous backing from the 11-member IFA board, initially on a two-year deal.
Fernandez's contract officially ends at the end of the year.
"I don't believe there has ever been such concensus over the choice of a coach as there is with Eli, everybody in the country, administrators, coaches, players and fans think he is the right man for the job," said Israeli FA chairman Avi Luzon.
Guttman's first task will be to prepare for a home international friendly against Euro 2012 co-hosts Ukraine on February 29, and to formulate a squad for the Brazil 2014 World Cup qualifying campaign that begins in September.
Israel have been drawn in European qualifying group F with Portugal, Russia, Azerbaijan, Northern Ireland and Luxembourg. They have qualified for a major finals only once, the 1970 World Cup finals in Mexico.
"This team's main code will be honour and respect, there will be no egos in the dressing room. It will always adhere to a playing system that I will determine because only through a disciplined system of play will it be possible to narrow the gaps against opposition such as Russia and Portugal," Guttman said.
The Israeli has coached many clubs in a 33-year career and began as an understudy to Shlomo Scharf, Israel's longest-serving coach between 1992-99 during their initial period in the European fray.
He had most success coaching Hapoel Haifa and Hapoel Tel Aviv, clubs with whom he has won two league championships and three State Cups. He also coached Cypriot sides Paralimni and AEL Limassol.
Fernandez, who was appointed in May 2010, was not retained after they finished eight points behind group F winners Greece in the Euro 2012 qualifiers.
The Frenchman was heavily criticised in the Israeli media, which said he had failed to establish a stable squad and made frequent and unorthodox changes to his line-ups.
