The Los Angeles Times reports that the two resigned after State Sen. Kevin De Leon criticized Gonzales and two other city council members for acting secretively.
On Oct. 18, Gonzales and two other council members voted to make Montgomery the permanent city attorney without placing the item on its agenda.
Gonzales submitted his resignation, but it won't become effective until his pension payments are confirmed by the California Public Employee System.
Gonzales has been a member of the city council since 1974 and mayor since 2009.
Montgomery will continue to act as attorney for the Vernon Redevelopment Agency and Vernon's Light & Power Department.
In August, the state senate narrowly voted against dissolving the city after three top officials were convicted of corruption charges.
The City News Service contributed to this report.