The 56-year-old Herrera, a former defender who led Mexico to the last 16 at the 2014 World Cup and a CONCACAF Gold Cup title in 2015, replaced Gustavo Alfaro who left in August to coach Paraguay.
Claudio Vivas, who had taken over as Costa Rica's interim manager, was sacked in November following the country's exit from the CONCACAF Nations League's quarter-finals.
Costa Rica are top of Group B in the second round of North America's World Cup qualifiers. They face Bahamas and Trinidad and Tobago in June as they bid to book a fourth World Cup finals appearance in a row.
